TSTP Solution File: SET651+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET651+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 05:27:52 EDT 2022
% Result : Theorem 1.46s 1.68s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of clauses : 47 ( 12 unt; 5 nHn; 47 RR)
% Number of literals : 124 ( 0 equ; 80 neg)
% Maximal clause size : 7 ( 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; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
ilf_type(u,set_type),
file('SET651+3.p',unknown),
[] ).
cnf(6,axiom,
subset(domain_of(skc8),skc6),
file('SET651+3.p',unknown),
[] ).
cnf(11,axiom,
ilf_type(skc8,relation_type(skc5,skc7)),
file('SET651+3.p',unknown),
[] ).
cnf(15,axiom,
~ ilf_type(skc8,relation_type(skc6,skc7)),
file('SET651+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ relation_like(u)
| ~ ilf_type(u,set_type)
| ilf_type(u,binary_relation_type) ),
file('SET651+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ ilf_type(u,binary_relation_type)
| subset(u,cross_product(domain_of(u),range_of(u))) ),
file('SET651+3.p',unknown),
[] ).
cnf(32,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET651+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf14(v,u),u)
| member(u,power_set(v)) ),
file('SET651+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,subset_type(cross_product(u,v)))
| relation_like(w) ),
file('SET651+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| subset(range_of(w),v) ),
file('SET651+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ ilf_type(u,member_type(power_set(v)))
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| ilf_type(u,subset_type(v)) ),
file('SET651+3.p',unknown),
[] ).
cnf(41,axiom,
( ~ member(skf14(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| member(v,power_set(u)) ),
file('SET651+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ member(u,v)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ilf_type(u,member_type(v))
| empty(v) ),
file('SET651+3.p',unknown),
[] ).
cnf(45,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('SET651+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ilf_type(u,relation_type(v,w)) ),
file('SET651+3.p',unknown),
[] ).
cnf(50,axiom,
( ~ subset(u,v)
| ~ ilf_type(w,set_type)
| ~ member(w,u)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(w,v) ),
file('SET651+3.p',unknown),
[] ).
cnf(51,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ subset(v,w)
| ~ subset(u,v)
| subset(u,w) ),
file('SET651+3.p',unknown),
[] ).
cnf(53,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(cross_product(u,w),cross_product(v,x)) ),
file('SET651+3.p',unknown),
[] ).
cnf(60,plain,
( ~ relation_like(u)
| ilf_type(u,binary_relation_type) ),
inference(mrr,[status(thm)],[24,5]),
[iquote('0:MRR:24.1,5.0')] ).
cnf(63,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[32,5]),
[iquote('0:MRR:32.1,32.3,5.0,5.0')] ).
cnf(66,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| relation_like(u) ),
inference(mrr,[status(thm)],[36,5]),
[iquote('0:MRR:36.0,36.1,5.0,5.0')] ).
cnf(67,plain,
( member(u,power_set(v))
| member(skf14(v,u),u) ),
inference(mrr,[status(thm)],[35,5]),
[iquote('0:MRR:35.0,35.1,5.0,5.0')] ).
cnf(69,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[43,5,63]),
[iquote('0:MRR:43.1,43.2,43.4,5.0,5.0,63.0')] ).
cnf(71,plain,
( ~ member(skf14(u,v),u)
| member(v,power_set(u)) ),
inference(mrr,[status(thm)],[41,5]),
[iquote('0:MRR:41.1,41.2,5.0,5.0')] ).
cnf(72,plain,
( ~ ilf_type(u,member_type(power_set(v)))
| ilf_type(u,subset_type(v)) ),
inference(mrr,[status(thm)],[40,5]),
[iquote('0:MRR:40.1,40.2,5.0,5.0')] ).
cnf(74,plain,
( ~ ilf_type(u,relation_type(v,w))
| subset(range_of(u),w) ),
inference(mrr,[status(thm)],[38,5]),
[iquote('0:MRR:38.0,38.1,5.0,5.0')] ).
cnf(77,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[45,5]),
[iquote('0:MRR:45.1,45.2,5.0,5.0')] ).
cnf(78,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| ilf_type(u,relation_type(v,w)) ),
inference(mrr,[status(thm)],[46,5]),
[iquote('0:MRR:46.1,46.2,5.0,5.0')] ).
cnf(82,plain,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
inference(mrr,[status(thm)],[50,5]),
[iquote('0:MRR:50.1,50.3,50.4,5.0,5.0,5.0')] ).
cnf(83,plain,
( ~ subset(u,v)
| ~ subset(v,w)
| subset(u,w) ),
inference(mrr,[status(thm)],[51,5]),
[iquote('0:MRR:51.0,51.1,51.2,5.0,5.0,5.0')] ).
cnf(85,plain,
( ~ subset(u,v)
| ~ subset(w,x)
| subset(cross_product(u,w),cross_product(v,x)) ),
inference(mrr,[status(thm)],[53,5]),
[iquote('0:MRR:53.0,53.1,53.2,53.3,5.0,5.0,5.0,5.0')] ).
cnf(91,plain,
ilf_type(skc8,subset_type(cross_product(skc5,skc7))),
inference(res,[status(thm),theory(equality)],[11,77]),
[iquote('0:Res:11.0,77.0')] ).
cnf(93,plain,
subset(range_of(skc8),skc7),
inference(res,[status(thm),theory(equality)],[11,74]),
[iquote('0:Res:11.0,74.0')] ).
cnf(94,plain,
~ ilf_type(skc8,subset_type(cross_product(skc6,skc7))),
inference(res,[status(thm),theory(equality)],[78,15]),
[iquote('0:Res:78.1,15.0')] ).
cnf(109,plain,
relation_like(skc8),
inference(res,[status(thm),theory(equality)],[91,66]),
[iquote('0:Res:91.0,66.0')] ).
cnf(120,plain,
( ~ member(u,power_set(v))
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[69,72]),
[iquote('0:Res:69.1,72.0')] ).
cnf(175,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ subset(cross_product(domain_of(u),range_of(u)),v)
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[27,83]),
[iquote('0:Res:27.1,83.0')] ).
cnf(183,plain,
( ~ subset(u,v)
| member(u,power_set(w))
| member(skf14(w,u),v) ),
inference(res,[status(thm),theory(equality)],[67,82]),
[iquote('0:Res:67.1,82.0')] ).
cnf(430,plain,
( ~ subset(u,v)
| member(u,power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[183,71]),
[iquote('0:Res:183.2,71.0')] ).
cnf(439,plain,
( ~ subset(u,v)
| member(u,power_set(v)) ),
inference(obv,[status(thm),theory(equality)],[430]),
[iquote('0:Obv:430.1')] ).
cnf(446,plain,
( ~ subset(u,v)
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[439,120]),
[iquote('0:Res:439.1,120.0')] ).
cnf(459,plain,
~ subset(skc8,cross_product(skc6,skc7)),
inference(res,[status(thm),theory(equality)],[446,94]),
[iquote('0:Res:446.1,94.0')] ).
cnf(488,plain,
( ~ subset(domain_of(u),v)
| ~ subset(range_of(u),w)
| ~ ilf_type(u,binary_relation_type)
| subset(u,cross_product(v,w)) ),
inference(res,[status(thm),theory(equality)],[85,175]),
[iquote('0:Res:85.2,175.1')] ).
cnf(4248,plain,
( ~ subset(domain_of(skc8),skc6)
| ~ subset(range_of(skc8),skc7)
| ~ ilf_type(skc8,binary_relation_type) ),
inference(res,[status(thm),theory(equality)],[488,459]),
[iquote('0:Res:488.3,459.0')] ).
cnf(4256,plain,
~ ilf_type(skc8,binary_relation_type),
inference(mrr,[status(thm)],[4248,6,93]),
[iquote('0:MRR:4248.0,4248.1,6.0,93.0')] ).
cnf(4257,plain,
~ relation_like(skc8),
inference(res,[status(thm),theory(equality)],[60,4256]),
[iquote('0:Res:60.1,4256.0')] ).
cnf(4258,plain,
$false,
inference(ssi,[status(thm)],[4257,109]),
[iquote('0:SSi:4257.0,109.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET651+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 08:21:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.46/1.68
% 1.46/1.68 SPASS V 3.9
% 1.46/1.68 SPASS beiseite: Proof found.
% 1.46/1.68 % SZS status Theorem
% 1.46/1.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.46/1.68 SPASS derived 4002 clauses, backtracked 0 clauses, performed 3 splits and kept 2810 clauses.
% 1.46/1.68 SPASS allocated 102735 KBytes.
% 1.46/1.68 SPASS spent 0:00:01.30 on the problem.
% 1.46/1.68 0:00:00.04 for the input.
% 1.46/1.68 0:00:00.04 for the FLOTTER CNF translation.
% 1.46/1.68 0:00:00.07 for inferences.
% 1.46/1.68 0:00:00.00 for the backtracking.
% 1.46/1.68 0:00:01.10 for the reduction.
% 1.46/1.68
% 1.46/1.68
% 1.46/1.68 Here is a proof with depth 6, length 47 :
% 1.46/1.68 % SZS output start Refutation
% See solution above
% 1.46/1.68 Formulae used in the proof : p26 prove_relset_1_13 p13 p2 p24 p18 p23 p6 p15 p20 p4 p9 p1 p3
% 1.46/1.68
%------------------------------------------------------------------------------