TSTP Solution File: SET632+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET632+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:27:41 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 30 ( 16 unt; 4 nHn; 30 RR)
% Number of literals : 47 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc5,skc3),
file('SET632+3.p',unknown),
[] ).
cnf(2,axiom,
subset(skc5,skc4),
file('SET632+3.p',unknown),
[] ).
cnf(3,axiom,
disjoint(skc3,skc4),
file('SET632+3.p',unknown),
[] ).
cnf(5,axiom,
~ equal(skc5,empty_set),
file('SET632+3.p',unknown),
[] ).
cnf(6,axiom,
~ member(u,empty_set),
file('SET632+3.p',unknown),
[] ).
cnf(8,axiom,
( empty(u)
| member(skf5(u),u) ),
file('SET632+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ empty(u)
| ~ member(v,u) ),
file('SET632+3.p',unknown),
[] ).
cnf(13,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET632+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ intersect(u,v)
| ~ disjoint(u,v) ),
file('SET632+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET632+3.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,v)
| ~ member(u,w)
| intersect(w,v) ),
file('SET632+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET632+3.p',unknown),
[] ).
cnf(21,plain,
~ intersect(skc3,skc4),
inference(res,[status(thm),theory(equality)],[3,14]),
[iquote('0:Res:3.0,14.0')] ).
cnf(23,plain,
( ~ member(u,skc5)
| member(u,skc4) ),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(26,plain,
( ~ member(u,skc5)
| member(u,skc3) ),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(28,plain,
( ~ subset(empty_set,skc5)
| ~ subset(skc5,empty_set) ),
inference(res,[status(thm),theory(equality)],[20,5]),
[iquote('0:Res:20.2,5.0')] ).
cnf(32,plain,
( empty(skc5)
| member(skf5(skc5),skc3) ),
inference(res,[status(thm),theory(equality)],[8,26]),
[iquote('0:Res:8.1,26.0')] ).
cnf(35,plain,
( empty(skc5)
| member(skf5(skc5),skc4) ),
inference(res,[status(thm),theory(equality)],[8,23]),
[iquote('0:Res:8.1,23.0')] ).
cnf(36,plain,
empty(skc5),
inference(spt,[spt(split,[position(s1)])],[35]),
[iquote('1:Spt:35.0')] ).
cnf(45,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[13,6]),
[iquote('0:Res:13.1,6.0')] ).
cnf(48,plain,
( ~ empty(u)
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[13,12]),
[iquote('0:Res:13.1,12.1')] ).
cnf(49,plain,
~ subset(skc5,empty_set),
inference(mrr,[status(thm)],[28,45]),
[iquote('0:MRR:28.0,45.0')] ).
cnf(51,plain,
~ empty(skc5),
inference(res,[status(thm),theory(equality)],[48,49]),
[iquote('0:Res:48.1,49.0')] ).
cnf(54,plain,
$false,
inference(ssi,[status(thm)],[51,36]),
[iquote('1:SSi:51.0,36.0')] ).
cnf(55,plain,
~ empty(skc5),
inference(spt,[spt(split,[position(sa)])],[54,36]),
[iquote('1:Spt:54.0,35.0,36.0')] ).
cnf(56,plain,
member(skf5(skc5),skc4),
inference(spt,[spt(split,[position(s2)])],[35]),
[iquote('1:Spt:54.0,35.1')] ).
cnf(58,plain,
member(skf5(skc5),skc3),
inference(mrr,[status(thm)],[32,55]),
[iquote('1:MRR:32.0,55.0')] ).
cnf(111,plain,
( ~ member(skf5(skc5),u)
| intersect(u,skc4) ),
inference(res,[status(thm),theory(equality)],[56,19]),
[iquote('1:Res:56.0,19.0')] ).
cnf(123,plain,
intersect(skc3,skc4),
inference(res,[status(thm),theory(equality)],[58,111]),
[iquote('1:Res:58.0,111.0')] ).
cnf(124,plain,
$false,
inference(mrr,[status(thm)],[123,21]),
[iquote('1:MRR:123.0,21.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET632+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 13:29:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 95 clauses, backtracked 5 clauses, performed 2 splits and kept 80 clauses.
% 0.19/0.45 SPASS allocated 97788 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.00 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 5, length 30 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : prove_th114 empty_set_defn empty_defn subset_defn disjoint_defn intersect_defn equal_defn
% 0.19/0.45
%------------------------------------------------------------------------------