TSTP Solution File: SET641+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET641+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 05:27:47 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 6 unt; 5 nHn; 25 RR)
% Number of literals : 64 ( 0 equ; 39 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; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
ilf_type(u,set_type),
file('SET641+3.p',unknown),
[] ).
cnf(9,axiom,
subset(skc3,cross_product(skc4,skc5)),
file('SET641+3.p',unknown),
[] ).
cnf(12,axiom,
~ ilf_type(skc3,relation_type(skc4,skc5)),
file('SET641+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET641+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf16(v,u),u)
| member(u,power_set(v)) ),
file('SET641+3.p',unknown),
[] ).
cnf(32,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('SET641+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ member(skf16(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| member(v,power_set(u)) ),
file('SET641+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ member(u,v)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ilf_type(u,member_type(v))
| empty(v) ),
file('SET641+3.p',unknown),
[] ).
cnf(37,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('SET641+3.p',unknown),
[] ).
cnf(40,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('SET641+3.p',unknown),
[] ).
cnf(53,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[26,4]),
[iquote('0:MRR:26.1,26.3,4.0,4.0')] ).
cnf(57,plain,
( member(u,power_set(v))
| member(skf16(v,u),u) ),
inference(mrr,[status(thm)],[29,4]),
[iquote('0:MRR:29.0,29.1,4.0,4.0')] ).
cnf(59,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[35,4,53]),
[iquote('0:MRR:35.1,35.2,35.4,4.0,4.0,53.0')] ).
cnf(61,plain,
( ~ member(skf16(u,v),u)
| member(v,power_set(u)) ),
inference(mrr,[status(thm)],[33,4]),
[iquote('0:MRR:33.1,33.2,4.0,4.0')] ).
cnf(62,plain,
( ~ ilf_type(u,member_type(power_set(v)))
| ilf_type(u,subset_type(v)) ),
inference(mrr,[status(thm)],[32,4]),
[iquote('0:MRR:32.1,32.2,4.0,4.0')] ).
cnf(65,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| ilf_type(u,relation_type(v,w)) ),
inference(mrr,[status(thm)],[37,4]),
[iquote('0:MRR:37.1,37.2,4.0,4.0')] ).
cnf(68,plain,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
inference(mrr,[status(thm)],[40,4]),
[iquote('0:MRR:40.1,40.3,40.4,4.0,4.0,4.0')] ).
cnf(75,plain,
~ ilf_type(skc3,subset_type(cross_product(skc4,skc5))),
inference(res,[status(thm),theory(equality)],[65,12]),
[iquote('0:Res:65.1,12.0')] ).
cnf(89,plain,
( ~ member(u,power_set(v))
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[59,62]),
[iquote('0:Res:59.1,62.0')] ).
cnf(119,plain,
( ~ subset(u,v)
| member(u,power_set(w))
| member(skf16(w,u),v) ),
inference(res,[status(thm),theory(equality)],[57,68]),
[iquote('0:Res:57.1,68.0')] ).
cnf(392,plain,
( ~ subset(u,v)
| member(u,power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[119,61]),
[iquote('0:Res:119.2,61.0')] ).
cnf(402,plain,
( ~ subset(u,v)
| member(u,power_set(v)) ),
inference(obv,[status(thm),theory(equality)],[392]),
[iquote('0:Obv:392.1')] ).
cnf(408,plain,
( ~ subset(u,v)
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[402,89]),
[iquote('0:Res:402.1,89.0')] ).
cnf(412,plain,
~ subset(skc3,cross_product(skc4,skc5)),
inference(res,[status(thm),theory(equality)],[408,75]),
[iquote('0:Res:408.1,75.0')] ).
cnf(413,plain,
$false,
inference(mrr,[status(thm)],[412,9]),
[iquote('0:MRR:412.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % 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 : Sun Jul 10 08:18:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.48
% 0.18/0.48 SPASS V 3.9
% 0.18/0.48 SPASS beiseite: Proof found.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 SPASS derived 317 clauses, backtracked 0 clauses, performed 0 splits and kept 274 clauses.
% 0.18/0.48 SPASS allocated 98040 KBytes.
% 0.18/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.48 0:00:00.03 for the input.
% 0.18/0.48 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.48 0:00:00.01 for inferences.
% 0.18/0.48 0:00:00.00 for the backtracking.
% 0.18/0.48 0:00:00.04 for the reduction.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Here is a proof with depth 4, length 25 :
% 0.18/0.48 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : p18 prove_relset_1_3 p14 p10 p7 p12 p1 p5
% 0.18/0.48
%------------------------------------------------------------------------------