TSTP Solution File: SET649+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET649+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 05:27:50 EDT 2022
% Result : Theorem 2.37s 2.58s
% Output : Refutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of clauses : 35 ( 8 unt; 5 nHn; 35 RR)
% Number of literals : 97 ( 0 equ; 63 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ilf_type(skc6,binary_relation_type),
file('SET649+3.p',unknown),
[] ).
cnf(5,axiom,
ilf_type(u,set_type),
file('SET649+3.p',unknown),
[] ).
cnf(6,axiom,
subset(domain_of(skc6),skc4),
file('SET649+3.p',unknown),
[] ).
cnf(7,axiom,
subset(range_of(skc6),skc5),
file('SET649+3.p',unknown),
[] ).
cnf(16,axiom,
~ ilf_type(skc6,relation_type(skc4,skc5)),
file('SET649+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ ilf_type(u,binary_relation_type)
| subset(u,cross_product(domain_of(u),range_of(u))) ),
file('SET649+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET649+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf19(v,u),u)
| member(u,power_set(v)) ),
file('SET649+3.p',unknown),
[] ).
cnf(39,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('SET649+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ member(skf19(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| member(v,power_set(u)) ),
file('SET649+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ member(u,v)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ilf_type(u,member_type(v))
| empty(v) ),
file('SET649+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('SET649+3.p',unknown),
[] ).
cnf(51,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('SET649+3.p',unknown),
[] ).
cnf(52,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('SET649+3.p',unknown),
[] ).
cnf(54,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('SET649+3.p',unknown),
[] ).
cnf(64,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[33,5]),
[iquote('0:MRR:33.1,33.3,5.0,5.0')] ).
cnf(67,plain,
( member(u,power_set(v))
| member(skf19(v,u),u) ),
inference(mrr,[status(thm)],[37,5]),
[iquote('0:MRR:37.0,37.1,5.0,5.0')] ).
cnf(70,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[42,5,64]),
[iquote('0:MRR:42.1,42.2,42.4,5.0,5.0,64.0')] ).
cnf(72,plain,
( ~ member(skf19(u,v),u)
| member(v,power_set(u)) ),
inference(mrr,[status(thm)],[40,5]),
[iquote('0:MRR:40.1,40.2,5.0,5.0')] ).
cnf(73,plain,
( ~ ilf_type(u,member_type(power_set(v)))
| ilf_type(u,subset_type(v)) ),
inference(mrr,[status(thm)],[39,5]),
[iquote('0:MRR:39.1,39.2,5.0,5.0')] ).
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(83,plain,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
inference(mrr,[status(thm)],[51,5]),
[iquote('0:MRR:51.1,51.3,51.4,5.0,5.0,5.0')] ).
cnf(84,plain,
( ~ subset(u,v)
| ~ subset(v,w)
| subset(u,w) ),
inference(mrr,[status(thm)],[52,5]),
[iquote('0:MRR:52.0,52.1,52.2,5.0,5.0,5.0')] ).
cnf(86,plain,
( ~ subset(u,v)
| ~ subset(w,x)
| subset(cross_product(u,w),cross_product(v,x)) ),
inference(mrr,[status(thm)],[54,5]),
[iquote('0:MRR:54.0,54.1,54.2,54.3,5.0,5.0,5.0,5.0')] ).
cnf(103,plain,
~ ilf_type(skc6,subset_type(cross_product(skc4,skc5))),
inference(res,[status(thm),theory(equality)],[78,16]),
[iquote('0:Res:78.1,16.0')] ).
cnf(144,plain,
( ~ member(u,power_set(v))
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[70,73]),
[iquote('0:Res:70.1,73.0')] ).
cnf(188,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)],[28,84]),
[iquote('0:Res:28.1,84.0')] ).
cnf(197,plain,
( ~ subset(u,v)
| member(u,power_set(w))
| member(skf19(w,u),v) ),
inference(res,[status(thm),theory(equality)],[67,83]),
[iquote('0:Res:67.1,83.0')] ).
cnf(624,plain,
( ~ subset(u,v)
| member(u,power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[197,72]),
[iquote('0:Res:197.2,72.0')] ).
cnf(635,plain,
( ~ subset(u,v)
| member(u,power_set(v)) ),
inference(obv,[status(thm),theory(equality)],[624]),
[iquote('0:Obv:624.1')] ).
cnf(695,plain,
( ~ subset(u,v)
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[635,144]),
[iquote('0:Res:635.1,144.0')] ).
cnf(698,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)],[86,188]),
[iquote('0:Res:86.2,188.1')] ).
cnf(703,plain,
~ subset(skc6,cross_product(skc4,skc5)),
inference(res,[status(thm),theory(equality)],[695,103]),
[iquote('0:Res:695.1,103.0')] ).
cnf(7457,plain,
( ~ subset(domain_of(skc6),skc4)
| ~ subset(range_of(skc6),skc5)
| ~ ilf_type(skc6,binary_relation_type) ),
inference(res,[status(thm),theory(equality)],[698,703]),
[iquote('0:Res:698.3,703.0')] ).
cnf(7481,plain,
$false,
inference(mrr,[status(thm)],[7457,6,7,1]),
[iquote('0:MRR:7457.0,7457.1,7457.2,6.0,7.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET649+3 : TPTP v8.1.0. Released v2.2.0.
% 0.14/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 19:50:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.37/2.58
% 2.37/2.58 SPASS V 3.9
% 2.37/2.58 SPASS beiseite: Proof found.
% 2.37/2.58 % SZS status Theorem
% 2.37/2.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.37/2.58 SPASS derived 7068 clauses, backtracked 242 clauses, performed 15 splits and kept 4450 clauses.
% 2.37/2.58 SPASS allocated 104991 KBytes.
% 2.37/2.58 SPASS spent 0:00:02.16 on the problem.
% 2.37/2.58 0:00:00.04 for the input.
% 2.37/2.58 0:00:00.04 for the FLOTTER CNF translation.
% 2.37/2.58 0:00:00.09 for inferences.
% 2.37/2.58 0:00:00.05 for the backtracking.
% 2.37/2.58 0:00:01.88 for the reduction.
% 2.37/2.58
% 2.37/2.58
% 2.37/2.58 Here is a proof with depth 5, length 35 :
% 2.37/2.58 % SZS output start Refutation
% See solution above
% 2.37/2.58 Formulae used in the proof : prove_relset_1_11 p26 p2 p24 p20 p15 p22 p4 p12 p1 p3
% 2.37/2.58
%------------------------------------------------------------------------------