TSTP Solution File: SET666+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 6 unt; 5 nHn; 29 RR)
% Number of literals : 74 ( 0 equ; 44 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 : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
ilf_type(u,set_type),
file('SET666+3.p',unknown),
[] ).
cnf(10,axiom,
~ ilf_type(identity_relation_of(skc2),identity_relation_of_type(skc2)),
file('SET666+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ ilf_type(u,set_type)
| subset(identity_relation_of(u),cross_product(u,u)) ),
file('SET666+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET666+3.p',unknown),
[] ).
cnf(30,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf14(v,u),u)
| member(u,power_set(v)) ),
file('SET666+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ ilf_type(u,relation_type(v,v))
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| ilf_type(u,identity_relation_of_type(v)) ),
file('SET666+3.p',unknown),
[] ).
cnf(35,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('SET666+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ member(skf14(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| member(v,power_set(u)) ),
file('SET666+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ member(u,v)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ilf_type(u,member_type(v))
| empty(v) ),
file('SET666+3.p',unknown),
[] ).
cnf(40,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('SET666+3.p',unknown),
[] ).
cnf(45,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('SET666+3.p',unknown),
[] ).
cnf(58,plain,
subset(identity_relation_of(u),cross_product(u,u)),
inference(mrr,[status(thm)],[18,3]),
[iquote('0:MRR:18.0,3.0')] ).
cnf(60,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[27,3]),
[iquote('0:MRR:27.1,27.3,3.0,3.0')] ).
cnf(64,plain,
( member(u,power_set(v))
| member(skf14(v,u),u) ),
inference(mrr,[status(thm)],[30,3]),
[iquote('0:MRR:30.0,30.1,3.0,3.0')] ).
cnf(66,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[38,3,60]),
[iquote('0:MRR:38.1,38.2,38.4,3.0,3.0,60.0')] ).
cnf(68,plain,
( ~ member(skf14(u,v),u)
| member(v,power_set(u)) ),
inference(mrr,[status(thm)],[36,3]),
[iquote('0:MRR:36.1,36.2,3.0,3.0')] ).
cnf(69,plain,
( ~ ilf_type(u,member_type(power_set(v)))
| ilf_type(u,subset_type(v)) ),
inference(mrr,[status(thm)],[35,3]),
[iquote('0:MRR:35.1,35.2,3.0,3.0')] ).
cnf(71,plain,
( ~ ilf_type(u,relation_type(v,v))
| ilf_type(u,identity_relation_of_type(v)) ),
inference(mrr,[status(thm)],[33,3]),
[iquote('0:MRR:33.1,33.2,3.0,3.0')] ).
cnf(74,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| ilf_type(u,relation_type(v,w)) ),
inference(mrr,[status(thm)],[40,3]),
[iquote('0:MRR:40.1,40.2,3.0,3.0')] ).
cnf(79,plain,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
inference(mrr,[status(thm)],[45,3]),
[iquote('0:MRR:45.1,45.3,45.4,3.0,3.0,3.0')] ).
cnf(82,plain,
~ ilf_type(identity_relation_of(skc2),relation_type(skc2,skc2)),
inference(res,[status(thm),theory(equality)],[71,10]),
[iquote('0:Res:71.1,10.0')] ).
cnf(97,plain,
( ~ member(u,power_set(v))
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[66,69]),
[iquote('0:Res:66.1,69.0')] ).
cnf(133,plain,
( ~ subset(u,v)
| member(u,power_set(w))
| member(skf14(w,u),v) ),
inference(res,[status(thm),theory(equality)],[64,79]),
[iquote('0:Res:64.1,79.0')] ).
cnf(303,plain,
( ~ subset(u,v)
| member(u,power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[133,68]),
[iquote('0:Res:133.2,68.0')] ).
cnf(310,plain,
( ~ subset(u,v)
| member(u,power_set(v)) ),
inference(obv,[status(thm),theory(equality)],[303]),
[iquote('0:Obv:303.1')] ).
cnf(316,plain,
( ~ subset(u,v)
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[310,97]),
[iquote('0:Res:310.1,97.0')] ).
cnf(318,plain,
( ~ subset(u,cross_product(v,w))
| ilf_type(u,relation_type(v,w)) ),
inference(res,[status(thm),theory(equality)],[316,74]),
[iquote('0:Res:316.1,74.0')] ).
cnf(356,plain,
ilf_type(identity_relation_of(u),relation_type(u,u)),
inference(res,[status(thm),theory(equality)],[58,318]),
[iquote('0:Res:58.0,318.0')] ).
cnf(357,plain,
$false,
inference(unc,[status(thm)],[356,82]),
[iquote('0:UnC:356.0,82.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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 : Sun Jul 10 17:11:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 260 clauses, backtracked 0 clauses, performed 0 splits and kept 238 clauses.
% 0.20/0.47 SPASS allocated 97954 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.03 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 5, length 29 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : p24 prove_relset_1_29 p3 p22 p16 p6 p12 p18 p1 p14
% 0.20/0.47
%------------------------------------------------------------------------------