TSTP Solution File: SET662+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 05:27:55 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 7 unt; 3 nHn; 19 RR)
% Number of literals : 42 ( 0 equ; 26 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 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(5,axiom,
ilf_type(u,set_type),
file('SET662+3.p',unknown),
[] ).
cnf(12,axiom,
~ ilf_type(empty_set,relation_type(skc2,skc3)),
file('SET662+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ ilf_type(u,set_type)
| ~ member(u,empty_set) ),
file('SET662+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET662+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf13(v,u),u)
| member(u,power_set(v)) ),
file('SET662+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('SET662+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('SET662+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('SET662+3.p',unknown),
[] ).
cnf(44,plain,
~ member(u,empty_set),
inference(mrr,[status(thm)],[14,5]),
[iquote('0:MRR:14.0,5.0')] ).
cnf(51,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[26,5]),
[iquote('0:MRR:26.1,26.3,5.0,5.0')] ).
cnf(55,plain,
( member(u,power_set(v))
| member(skf13(v,u),u) ),
inference(mrr,[status(thm)],[29,5]),
[iquote('0:MRR:29.0,29.1,5.0,5.0')] ).
cnf(57,plain,
( ~ member(u,v)
| ilf_type(u,member_type(v)) ),
inference(mrr,[status(thm)],[35,5,51]),
[iquote('0:MRR:35.1,35.2,35.4,5.0,5.0,51.0')] ).
cnf(60,plain,
( ~ ilf_type(u,member_type(power_set(v)))
| ilf_type(u,subset_type(v)) ),
inference(mrr,[status(thm)],[32,5]),
[iquote('0:MRR:32.1,32.2,5.0,5.0')] ).
cnf(63,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| ilf_type(u,relation_type(v,w)) ),
inference(mrr,[status(thm)],[37,5]),
[iquote('0:MRR:37.1,37.2,5.0,5.0')] ).
cnf(68,plain,
~ ilf_type(empty_set,subset_type(cross_product(skc2,skc3))),
inference(res,[status(thm),theory(equality)],[63,12]),
[iquote('0:Res:63.1,12.0')] ).
cnf(76,plain,
member(empty_set,power_set(u)),
inference(res,[status(thm),theory(equality)],[55,44]),
[iquote('0:Res:55.1,44.0')] ).
cnf(85,plain,
( ~ member(u,power_set(v))
| ilf_type(u,subset_type(v)) ),
inference(res,[status(thm),theory(equality)],[57,60]),
[iquote('0:Res:57.1,60.0')] ).
cnf(94,plain,
ilf_type(empty_set,subset_type(u)),
inference(res,[status(thm),theory(equality)],[76,85]),
[iquote('0:Res:76.0,85.0')] ).
cnf(95,plain,
$false,
inference(unc,[status(thm)],[94,68]),
[iquote('0:UnC:94.0,68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 03:42:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 24 clauses, backtracked 0 clauses, performed 0 splits and kept 48 clauses.
% 0.19/0.46 SPASS allocated 97769 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.00 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 2, length 19 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : p20 prove_relset_1_25 p4 p11 p12 p7 p14 p2
% 0.19/0.46
%------------------------------------------------------------------------------