TSTP Solution File: SET648+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET648+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 0.48s 0.63s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of clauses : 35 ( 7 unt; 5 nHn; 35 RR)
% Number of literals : 91 ( 0 equ; 55 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ilf_type(skc4,binary_relation_type),
file('SET648+3.p',unknown),
[] ).
cnf(4,axiom,
ilf_type(u,set_type),
file('SET648+3.p',unknown),
[] ).
cnf(5,axiom,
subset(range_of(skc4),skc3),
file('SET648+3.p',unknown),
[] ).
cnf(14,axiom,
~ ilf_type(skc4,relation_type(domain_of(skc4),skc3)),
file('SET648+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ ilf_type(u,binary_relation_type)
| subset(u,cross_product(domain_of(u),range_of(u))) ),
file('SET648+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET648+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf19(v,u),u)
| member(u,power_set(v)) ),
file('SET648+3.p',unknown),
[] ).
cnf(37,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('SET648+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ member(skf19(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| member(v,power_set(u)) ),
file('SET648+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ member(u,v)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ilf_type(u,member_type(v))
| empty(v) ),
file('SET648+3.p',unknown),
[] ).
cnf(44,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('SET648+3.p',unknown),
[] ).
cnf(49,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('SET648+3.p',unknown),
[] ).
cnf(50,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ subset(u,v)
| subset(cross_product(w,u),cross_product(w,v)) ),
file('SET648+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('SET648+3.p',unknown),
[] ).
cnf(63,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[31,4]),
[iquote('0:MRR:31.1,31.3,4.0,4.0')] ).
cnf(66,plain,
( member(u,power_set(v))
| member(skf19(v,u),u) ),
inference(mrr,[status(thm)],[35,4]),
[iquote('0:MRR:35.0,35.1,4.0,4.0')] ).
cnf(69,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[40,4,63]),
[iquote('0:MRR:40.1,40.2,40.4,4.0,4.0,63.0')] ).
cnf(71,plain,
( ~ member(skf19(u,v),u)
| member(v,power_set(u)) ),
inference(mrr,[status(thm)],[38,4]),
[iquote('0:MRR:38.1,38.2,4.0,4.0')] ).
cnf(72,plain,
( ~ ilf_type(u,member_type(power_set(v)))
| ilf_type(u,subset_type(v)) ),
inference(mrr,[status(thm)],[37,4]),
[iquote('0:MRR:37.1,37.2,4.0,4.0')] ).
cnf(77,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| ilf_type(u,relation_type(v,w)) ),
inference(mrr,[status(thm)],[44,4]),
[iquote('0:MRR:44.1,44.2,4.0,4.0')] ).
cnf(82,plain,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
inference(mrr,[status(thm)],[49,4]),
[iquote('0:MRR:49.1,49.3,49.4,4.0,4.0,4.0')] ).
cnf(83,plain,
( ~ subset(u,v)
| subset(cross_product(w,u),cross_product(w,v)) ),
inference(mrr,[status(thm)],[50,4]),
[iquote('0:MRR:50.0,50.1,50.2,4.0,4.0,4.0')] ).
cnf(85,plain,
( ~ subset(u,v)
| ~ subset(v,w)
| subset(u,w) ),
inference(mrr,[status(thm)],[52,4]),
[iquote('0:MRR:52.0,52.1,52.2,4.0,4.0,4.0')] ).
cnf(87,plain,
subset(skc4,cross_product(domain_of(skc4),range_of(skc4))),
inference(res,[status(thm),theory(equality)],[1,26]),
[iquote('0:Res:1.0,26.0')] ).
cnf(125,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(166,plain,
( ~ subset(cross_product(domain_of(skc4),range_of(skc4)),u)
| subset(skc4,u) ),
inference(res,[status(thm),theory(equality)],[87,85]),
[iquote('0:Res:87.0,85.0')] ).
cnf(174,plain,
( ~ subset(u,v)
| member(u,power_set(w))
| member(skf19(w,u),v) ),
inference(res,[status(thm),theory(equality)],[66,82]),
[iquote('0:Res:66.1,82.0')] ).
cnf(364,plain,
( ~ subset(range_of(skc4),u)
| subset(skc4,cross_product(domain_of(skc4),u)) ),
inference(res,[status(thm),theory(equality)],[83,166]),
[iquote('0:Res:83.1,166.0')] ).
cnf(545,plain,
( ~ subset(u,v)
| member(u,power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[174,71]),
[iquote('0:Res:174.2,71.0')] ).
cnf(556,plain,
( ~ subset(u,v)
| member(u,power_set(v)) ),
inference(obv,[status(thm),theory(equality)],[545]),
[iquote('0:Obv:545.1')] ).
cnf(625,plain,
( ~ subset(u,v)
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[556,125]),
[iquote('0:Res:556.1,125.0')] ).
cnf(627,plain,
( ~ subset(u,cross_product(v,w))
| ilf_type(u,relation_type(v,w)) ),
inference(res,[status(thm),theory(equality)],[625,77]),
[iquote('0:Res:625.1,77.0')] ).
cnf(1064,plain,
( ~ subset(range_of(skc4),u)
| ilf_type(skc4,relation_type(domain_of(skc4),u)) ),
inference(res,[status(thm),theory(equality)],[364,627]),
[iquote('0:Res:364.1,627.0')] ).
cnf(1098,plain,
~ subset(range_of(skc4),skc3),
inference(res,[status(thm),theory(equality)],[1064,14]),
[iquote('0:Res:1064.1,14.0')] ).
cnf(1100,plain,
$false,
inference(mrr,[status(thm)],[1098,5]),
[iquote('0:MRR:1098.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET648+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 04:10:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.63
% 0.48/0.63 SPASS V 3.9
% 0.48/0.63 SPASS beiseite: Proof found.
% 0.48/0.63 % SZS status Theorem
% 0.48/0.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.63 SPASS derived 953 clauses, backtracked 74 clauses, performed 2 splits and kept 702 clauses.
% 0.48/0.63 SPASS allocated 98659 KBytes.
% 0.48/0.63 SPASS spent 0:00:00.28 on the problem.
% 0.48/0.63 0:00:00.04 for the input.
% 0.48/0.63 0:00:00.04 for the FLOTTER CNF translation.
% 0.48/0.63 0:00:00.02 for inferences.
% 0.48/0.63 0:00:00.00 for the backtracking.
% 0.48/0.63 0:00:00.15 for the reduction.
% 0.48/0.63
% 0.48/0.63
% 0.48/0.63 Here is a proof with depth 6, length 35 :
% 0.48/0.63 % SZS output start Refutation
% See solution above
% 0.48/0.63 Formulae used in the proof : prove_relset_1_10 p26 p2 p24 p20 p15 p22 p4 p12 p3 p1
% 0.48/0.63
%------------------------------------------------------------------------------