TSTP Solution File: SET143+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET143+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:24:27 EDT 2022
% Result : Theorem 6.34s 6.51s
% Output : Refutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 38 ( 12 unt; 13 nHn; 38 RR)
% Number of literals : 77 ( 0 equ; 32 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 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(4,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET143+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET143+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET143+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET143+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET143+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET143+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET143+3.p',unknown),
[] ).
cnf(13,axiom,
~ equal(intersection(intersection(skc5,skc4),skc3),intersection(skc5,intersection(skc4,skc3))),
file('SET143+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET143+3.p',unknown),
[] ).
cnf(17,plain,
~ equal(intersection(skc5,intersection(skc3,skc4)),intersection(skc3,intersection(skc4,skc5))),
inference(rew,[status(thm),theory(equality)],[4,13]),
[iquote('0:Rew:4.0,13.0,4.0,13.0,4.0,13.0')] ).
cnf(21,plain,
( ~ subset(intersection(skc5,intersection(skc3,skc4)),intersection(skc3,intersection(skc4,skc5)))
| ~ subset(intersection(skc3,intersection(skc4,skc5)),intersection(skc5,intersection(skc3,skc4))) ),
inference(res,[status(thm),theory(equality)],[9,17]),
[iquote('0:Res:9.2,17.0')] ).
cnf(32,plain,
( subset(intersection(u,v),w)
| member(skf2(w,intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[5,7]),
[iquote('0:Res:5.1,7.0')] ).
cnf(35,plain,
( subset(intersection(u,v),w)
| member(skf2(w,intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[5,6]),
[iquote('0:Res:5.1,6.0')] ).
cnf(38,plain,
( ~ subset(u,v)
| subset(u,w)
| member(skf2(w,u),v) ),
inference(res,[status(thm),theory(equality)],[5,10]),
[iquote('0:Res:5.1,10.0')] ).
cnf(43,plain,
( subset(intersection(u,intersection(v,w)),x)
| member(skf2(x,intersection(u,intersection(v,w))),v) ),
inference(res,[status(thm),theory(equality)],[32,6]),
[iquote('0:Res:32.1,6.0')] ).
cnf(55,plain,
( ~ member(skf2(intersection(u,v),w),u)
| ~ member(skf2(intersection(u,v),w),v)
| subset(x,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[14,8]),
[iquote('0:Res:14.2,8.0')] ).
cnf(85,plain,
( subset(intersection(intersection(u,v),w),x)
| member(skf2(x,intersection(intersection(u,v),w)),u) ),
inference(res,[status(thm),theory(equality)],[35,6]),
[iquote('0:Res:35.1,6.0')] ).
cnf(86,plain,
( subset(intersection(intersection(u,v),w),x)
| member(skf2(x,intersection(intersection(u,v),w)),v) ),
inference(res,[status(thm),theory(equality)],[35,7]),
[iquote('0:Res:35.1,7.0')] ).
cnf(137,plain,
( subset(intersection(u,intersection(v,w)),v)
| subset(x,v) ),
inference(res,[status(thm),theory(equality)],[43,8]),
[iquote('0:Res:43.1,8.0')] ).
cnf(141,plain,
subset(intersection(u,intersection(v,w)),v),
inference(con,[status(thm)],[137]),
[iquote('0:Con:137.1')] ).
cnf(142,plain,
subset(intersection(u,intersection(v,w)),w),
inference(spr,[status(thm),theory(equality)],[4,141]),
[iquote('0:SpR:4.0,141.0')] ).
cnf(361,plain,
( ~ member(skf2(intersection(u,v),intersection(w,u)),v)
| subset(intersection(w,u),intersection(u,v))
| subset(x,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[32,55]),
[iquote('0:Res:32.1,55.0')] ).
cnf(363,plain,
( ~ subset(u,v)
| ~ member(skf2(intersection(v,w),u),w)
| subset(u,intersection(v,w))
| subset(x,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[38,55]),
[iquote('0:Res:38.2,55.0')] ).
cnf(367,plain,
( ~ subset(u,v)
| ~ member(skf2(intersection(v,w),u),w)
| subset(u,intersection(v,w)) ),
inference(con,[status(thm)],[363]),
[iquote('0:Con:363.3')] ).
cnf(369,plain,
( ~ member(skf2(intersection(u,v),intersection(w,u)),v)
| subset(intersection(w,u),intersection(u,v)) ),
inference(con,[status(thm)],[361]),
[iquote('0:Con:361.2')] ).
cnf(2014,plain,
( ~ subset(u,v)
| ~ subset(u,w)
| subset(u,intersection(w,v))
| subset(u,intersection(w,v)) ),
inference(res,[status(thm),theory(equality)],[38,367]),
[iquote('0:Res:38.2,367.1')] ).
cnf(2024,plain,
( ~ subset(u,v)
| ~ subset(u,w)
| subset(u,intersection(w,v)) ),
inference(obv,[status(thm),theory(equality)],[2014]),
[iquote('0:Obv:2014.2')] ).
cnf(2236,plain,
( subset(intersection(intersection(u,v),w),intersection(w,u))
| subset(intersection(intersection(u,v),w),intersection(w,u)) ),
inference(res,[status(thm),theory(equality)],[85,369]),
[iquote('0:Res:85.1,369.0')] ).
cnf(2242,plain,
( subset(intersection(intersection(u,v),w),intersection(w,v))
| subset(intersection(intersection(u,v),w),intersection(w,v)) ),
inference(res,[status(thm),theory(equality)],[86,369]),
[iquote('0:Res:86.1,369.0')] ).
cnf(2254,plain,
subset(intersection(intersection(u,v),w),intersection(w,u)),
inference(obv,[status(thm),theory(equality)],[2236]),
[iquote('0:Obv:2236.0')] ).
cnf(2257,plain,
subset(intersection(intersection(u,v),w),intersection(w,v)),
inference(obv,[status(thm),theory(equality)],[2242]),
[iquote('0:Obv:2242.0')] ).
cnf(2322,plain,
subset(intersection(u,intersection(v,w)),intersection(u,v)),
inference(spr,[status(thm),theory(equality)],[4,2254]),
[iquote('0:SpR:4.0,2254.0')] ).
cnf(2349,plain,
subset(intersection(intersection(u,v),w),intersection(v,w)),
inference(spr,[status(thm),theory(equality)],[4,2257]),
[iquote('0:SpR:4.0,2257.0')] ).
cnf(2540,plain,
subset(intersection(u,intersection(v,w)),intersection(w,u)),
inference(spr,[status(thm),theory(equality)],[4,2349]),
[iquote('0:SpR:4.0,2349.0')] ).
cnf(9436,plain,
( ~ subset(intersection(skc5,intersection(skc3,skc4)),intersection(skc4,skc5))
| ~ subset(intersection(skc5,intersection(skc3,skc4)),skc3)
| ~ subset(intersection(skc3,intersection(skc4,skc5)),intersection(skc5,intersection(skc3,skc4))) ),
inference(res,[status(thm),theory(equality)],[2024,21]),
[iquote('0:Res:2024.2,21.0')] ).
cnf(9484,plain,
~ subset(intersection(skc3,intersection(skc4,skc5)),intersection(skc5,intersection(skc3,skc4))),
inference(mrr,[status(thm)],[9436,2540,141]),
[iquote('0:MRR:9436.0,9436.1,2540.0,141.0')] ).
cnf(16620,plain,
( ~ subset(intersection(skc3,intersection(skc4,skc5)),intersection(skc3,skc4))
| ~ subset(intersection(skc3,intersection(skc4,skc5)),skc5) ),
inference(res,[status(thm),theory(equality)],[2024,9484]),
[iquote('0:Res:2024.2,9484.0')] ).
cnf(16627,plain,
$false,
inference(mrr,[status(thm)],[16620,2322,142]),
[iquote('0:MRR:16620.0,16620.1,2322.0,142.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET143+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 : Mon Jul 11 01:38:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.34/6.51
% 6.34/6.51 SPASS V 3.9
% 6.34/6.51 SPASS beiseite: Proof found.
% 6.34/6.51 % SZS status Theorem
% 6.34/6.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.34/6.51 SPASS derived 13444 clauses, backtracked 0 clauses, performed 0 splits and kept 3664 clauses.
% 6.34/6.51 SPASS allocated 95635 KBytes.
% 6.34/6.51 SPASS spent 0:00:06.06 on the problem.
% 6.34/6.51 0:00:00.03 for the input.
% 6.34/6.51 0:00:00.03 for the FLOTTER CNF translation.
% 6.34/6.51 0:00:00.14 for inferences.
% 6.34/6.51 0:00:00.00 for the backtracking.
% 6.34/6.51 0:00:05.81 for the reduction.
% 6.34/6.51
% 6.34/6.51
% 6.34/6.51 Here is a proof with depth 5, length 38 :
% 6.34/6.51 % SZS output start Refutation
% See solution above
% 6.34/6.51 Formulae used in the proof : commutativity_of_intersection subset_defn intersection_defn equal_defn prove_associativity_of_intersection
% 6.34/6.51
%------------------------------------------------------------------------------