TSTP Solution File: SET598+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 05:27:17 EDT 2022
% Result : Theorem 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 37 ( 17 unt; 4 nHn; 37 RR)
% Number of literals : 73 ( 0 equ; 40 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc7,skc5),
file('SET598+3.p',unknown),
[] ).
cnf(3,axiom,
subset(intersection(u,v),u),
file('SET598+3.p',unknown),
[] ).
cnf(6,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET598+3.p',unknown),
[] ).
cnf(7,axiom,
( subset(skc4,skc5)
| equal(intersection(skc5,skc6),skc4) ),
file('SET598+3.p',unknown),
[] ).
cnf(8,axiom,
( subset(skc4,skc6)
| equal(intersection(skc5,skc6),skc4) ),
file('SET598+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET598+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ subset(u,v)
| ~ subset(u,w)
| subset(u,intersection(w,v)) ),
file('SET598+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ subset(u,skc6)
| ~ subset(u,skc5)
| subset(u,skc4)
| equal(intersection(skc5,skc6),skc4) ),
file('SET598+3.p',unknown),
[] ).
cnf(22,axiom,
( ~ subset(skc4,skc6)
| ~ subset(skc4,skc5)
| ~ equal(intersection(skc5,skc6),skc4)
| subset(skc7,skc6) ),
file('SET598+3.p',unknown),
[] ).
cnf(23,axiom,
( ~ subset(skc4,skc6)
| ~ subset(skc4,skc5)
| ~ subset(skc7,skc4)
| ~ equal(intersection(skc5,skc6),skc4) ),
file('SET598+3.p',unknown),
[] ).
cnf(25,plain,
( ~ subset(skc7,u)
| subset(skc7,intersection(skc5,u)) ),
inference(res,[status(thm),theory(equality)],[1,17]),
[iquote('0:Res:1.0,17.0')] ).
cnf(34,plain,
( ~ subset(intersection(skc6,u),skc5)
| subset(intersection(skc6,u),skc4)
| equal(intersection(skc5,skc6),skc4) ),
inference(res,[status(thm),theory(equality)],[3,21]),
[iquote('0:Res:3.0,21.1')] ).
cnf(39,plain,
equal(intersection(skc5,skc6),skc4),
inference(spt,[spt(split,[position(s1)])],[21]),
[iquote('1:Spt:21.3')] ).
cnf(40,plain,
( ~ subset(skc4,skc6)
| ~ subset(skc4,skc5)
| ~ subset(skc7,skc4)
| ~ equal(skc4,skc4) ),
inference(rew,[status(thm),theory(equality)],[39,23]),
[iquote('1:Rew:39.0,23.3')] ).
cnf(41,plain,
( ~ subset(skc4,skc6)
| ~ subset(skc4,skc5)
| ~ equal(skc4,skc4)
| subset(skc7,skc6) ),
inference(rew,[status(thm),theory(equality)],[39,22]),
[iquote('1:Rew:39.0,22.2')] ).
cnf(42,plain,
( ~ subset(skc4,skc6)
| ~ subset(skc4,skc5)
| subset(skc7,skc6) ),
inference(obv,[status(thm),theory(equality)],[41]),
[iquote('1:Obv:41.2')] ).
cnf(43,plain,
( ~ subset(skc4,skc6)
| ~ subset(skc4,skc5)
| ~ subset(skc7,skc4) ),
inference(obv,[status(thm),theory(equality)],[40]),
[iquote('1:Obv:40.3')] ).
cnf(45,plain,
subset(skc4,skc5),
inference(spr,[status(thm),theory(equality)],[39,3]),
[iquote('1:SpR:39.0,3.0')] ).
cnf(46,plain,
( ~ subset(skc4,skc6)
| subset(skc7,skc6) ),
inference(mrr,[status(thm)],[42,45]),
[iquote('1:MRR:42.1,45.0')] ).
cnf(47,plain,
( ~ subset(skc4,skc6)
| ~ subset(skc7,skc4) ),
inference(mrr,[status(thm)],[43,45]),
[iquote('1:MRR:43.1,45.0')] ).
cnf(49,plain,
subset(intersection(u,v),v),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(57,plain,
subset(skc4,skc6),
inference(spr,[status(thm),theory(equality)],[39,49]),
[iquote('1:SpR:39.0,49.0')] ).
cnf(60,plain,
subset(skc7,skc6),
inference(mrr,[status(thm)],[46,57]),
[iquote('1:MRR:46.0,57.0')] ).
cnf(61,plain,
~ subset(skc7,skc4),
inference(mrr,[status(thm)],[47,57]),
[iquote('1:MRR:47.0,57.0')] ).
cnf(64,plain,
( ~ subset(skc7,skc6)
| subset(skc7,skc4) ),
inference(spr,[status(thm),theory(equality)],[39,25]),
[iquote('1:SpR:39.0,25.1')] ).
cnf(67,plain,
$false,
inference(mrr,[status(thm)],[64,60,61]),
[iquote('1:MRR:64.0,64.1,60.0,61.0')] ).
cnf(68,plain,
~ equal(intersection(skc5,skc6),skc4),
inference(spt,[spt(split,[position(sa)])],[67,39]),
[iquote('1:Spt:67.0,21.3,39.0')] ).
cnf(69,plain,
( ~ subset(u,skc6)
| ~ subset(u,skc5)
| subset(u,skc4) ),
inference(spt,[spt(split,[position(s2)])],[21]),
[iquote('1:Spt:67.0,21.0,21.1,21.2')] ).
cnf(70,plain,
subset(skc4,skc6),
inference(mrr,[status(thm)],[8,68]),
[iquote('1:MRR:8.1,68.0')] ).
cnf(71,plain,
subset(skc4,skc5),
inference(mrr,[status(thm)],[7,68]),
[iquote('1:MRR:7.1,68.0')] ).
cnf(75,plain,
( ~ subset(intersection(skc6,u),skc5)
| subset(intersection(skc6,u),skc4) ),
inference(mrr,[status(thm)],[34,68]),
[iquote('1:MRR:34.2,68.0')] ).
cnf(100,plain,
subset(intersection(skc6,skc5),skc4),
inference(res,[status(thm),theory(equality)],[49,75]),
[iquote('1:Res:49.0,75.0')] ).
cnf(101,plain,
subset(intersection(skc5,skc6),skc4),
inference(rew,[status(thm),theory(equality)],[6,100]),
[iquote('1:Rew:6.0,100.0')] ).
cnf(119,plain,
( ~ subset(skc4,intersection(skc5,skc6))
| equal(intersection(skc5,skc6),skc4) ),
inference(res,[status(thm),theory(equality)],[101,14]),
[iquote('1:Res:101.0,14.0')] ).
cnf(124,plain,
~ subset(skc4,intersection(skc5,skc6)),
inference(mrr,[status(thm)],[119,68]),
[iquote('1:MRR:119.1,68.0')] ).
cnf(176,plain,
( ~ subset(skc4,skc6)
| ~ subset(skc4,skc5) ),
inference(res,[status(thm),theory(equality)],[17,124]),
[iquote('1:Res:17.2,124.0')] ).
cnf(177,plain,
$false,
inference(mrr,[status(thm)],[176,70,71]),
[iquote('1:MRR:176.0,176.1,70.0,71.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jul 11 08:45:40 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.22/0.47
% 0.22/0.47 SPASS V 3.9
% 0.22/0.47 SPASS beiseite: Proof found.
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.47 SPASS derived 134 clauses, backtracked 11 clauses, performed 1 splits and kept 93 clauses.
% 0.22/0.47 SPASS allocated 85343 KBytes.
% 0.22/0.47 SPASS spent 0:00:00.10 on the problem.
% 0.22/0.47 0:00:00.03 for the input.
% 0.22/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.47 0:00:00.00 for inferences.
% 0.22/0.47 0:00:00.00 for the backtracking.
% 0.22/0.47 0:00:00.01 for the reduction.
% 0.22/0.47
% 0.22/0.47
% 0.22/0.47 Here is a proof with depth 4, length 37 :
% 0.22/0.47 % SZS output start Refutation
% See solution above
% 0.22/0.47 Formulae used in the proof : prove_th57 reflexivity_of_subset intersection_is_subset commutativity_of_intersection equal_defn intersection_of_subsets
% 0.22/0.47
%------------------------------------------------------------------------------