TSTP Solution File: SET578+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 05:27:04 EDT 2022
% Result : Theorem 7.29s 7.45s
% Output : Refutation 7.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 60 ( 12 unt; 26 nHn; 60 RR)
% Number of literals : 134 ( 0 equ; 43 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ equal(intersection(skc4,skc5),skc3),
file('SET578+3.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,skc3)
| member(u,skc4) ),
file('SET578+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,skc3)
| member(u,skc5) ),
file('SET578+3.p',unknown),
[] ).
cnf(7,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET578+3.p',unknown),
[] ).
cnf(8,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET578+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET578+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET578+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET578+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,skc5)
| ~ member(u,skc4)
| member(u,skc3) ),
file('SET578+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET578+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET578+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET578+3.p',unknown),
[] ).
cnf(18,axiom,
( equal(u,v)
| member(skf3(v,u),v)
| member(skf3(v,u),u) ),
file('SET578+3.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(skf3(u,v),u)
| ~ member(skf3(u,v),v)
| equal(v,u) ),
file('SET578+3.p',unknown),
[] ).
cnf(20,plain,
( ~ subset(skc3,intersection(skc4,skc5))
| ~ subset(intersection(skc4,skc5),skc3) ),
inference(res,[status(thm),theory(equality)],[13,2]),
[iquote('0:Res:13.2,2.0')] ).
cnf(30,plain,
( ~ member(skf2(skc5,u),skc3)
| subset(v,skc5) ),
inference(res,[status(thm),theory(equality)],[4,11]),
[iquote('0:Res:4.1,11.0')] ).
cnf(34,plain,
( subset(skc3,skc5)
| subset(u,skc5) ),
inference(res,[status(thm),theory(equality)],[8,30]),
[iquote('0:Res:8.1,30.0')] ).
cnf(35,plain,
subset(skc3,skc5),
inference(con,[status(thm)],[34]),
[iquote('0:Con:34.1')] ).
cnf(38,plain,
( subset(intersection(u,v),w)
| member(skf2(w,intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[8,10]),
[iquote('0:Res:8.1,10.0')] ).
cnf(43,plain,
( subset(intersection(u,v),w)
| member(skf2(w,intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.0')] ).
cnf(76,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)],[17,11]),
[iquote('0:Res:17.2,11.0')] ).
cnf(88,plain,
( equal(u,intersection(v,w))
| member(skf3(intersection(v,w),u),u)
| member(skf3(intersection(v,w),u),v) ),
inference(res,[status(thm),theory(equality)],[18,9]),
[iquote('0:Res:18.1,9.0')] ).
cnf(89,plain,
( equal(u,intersection(v,w))
| member(skf3(intersection(v,w),u),u)
| member(skf3(intersection(v,w),u),w) ),
inference(res,[status(thm),theory(equality)],[18,10]),
[iquote('0:Res:18.1,10.0')] ).
cnf(90,plain,
( ~ subset(u,v)
| equal(w,u)
| member(skf3(u,w),w)
| member(skf3(u,w),v) ),
inference(res,[status(thm),theory(equality)],[18,14]),
[iquote('0:Res:18.1,14.0')] ).
cnf(94,plain,
( equal(intersection(u,v),w)
| member(skf3(w,intersection(u,v)),w)
| member(skf3(w,intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[18,9]),
[iquote('0:Res:18.2,9.0')] ).
cnf(119,plain,
( ~ member(skf3(intersection(u,v),w),u)
| ~ member(skf3(intersection(u,v),w),v)
| ~ member(skf3(intersection(u,v),w),w)
| equal(w,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[17,19]),
[iquote('0:Res:17.2,19.0')] ).
cnf(126,plain,
( ~ member(skf2(u,intersection(v,skc5)),skc4)
| subset(intersection(v,skc5),u)
| member(skf2(u,intersection(v,skc5)),skc3) ),
inference(res,[status(thm),theory(equality)],[38,12]),
[iquote('0:Res:38.1,12.0')] ).
cnf(148,plain,
( subset(intersection(intersection(u,v),w),x)
| member(skf2(x,intersection(intersection(u,v),w)),v) ),
inference(res,[status(thm),theory(equality)],[43,10]),
[iquote('0:Res:43.1,10.0')] ).
cnf(262,plain,
( equal(u,skc3)
| member(skf3(skc3,u),u)
| member(skf3(skc3,u),skc5) ),
inference(res,[status(thm),theory(equality)],[35,90]),
[iquote('0:Res:35.0,90.0')] ).
cnf(348,plain,
( equal(intersection(u,v),u)
| member(skf3(intersection(u,v),u),u) ),
inference(fac,[status(thm)],[88]),
[iquote('0:Fac:88.1,88.2')] ).
cnf(410,plain,
( equal(intersection(u,v),v)
| member(skf3(intersection(u,v),v),v) ),
inference(fac,[status(thm)],[89]),
[iquote('0:Fac:89.1,89.2')] ).
cnf(460,plain,
( equal(intersection(u,v),u)
| member(skf3(u,intersection(u,v)),u) ),
inference(fac,[status(thm)],[94]),
[iquote('0:Fac:94.1,94.2')] ).
cnf(487,plain,
( ~ member(skf3(u,intersection(u,v)),intersection(u,v))
| equal(intersection(u,v),u)
| equal(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[460,19]),
[iquote('0:Res:460.1,19.0')] ).
cnf(488,plain,
( ~ member(skf3(u,intersection(u,v)),intersection(u,v))
| equal(intersection(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[487]),
[iquote('0:Obv:487.1')] ).
cnf(766,plain,
( ~ member(skf3(u,intersection(u,v)),u)
| ~ member(skf3(u,intersection(u,v)),v)
| equal(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[17,488]),
[iquote('0:Res:17.2,488.0')] ).
cnf(771,plain,
( ~ member(skf3(u,intersection(u,v)),v)
| equal(intersection(u,v),u) ),
inference(mrr,[status(thm)],[766,460]),
[iquote('0:MRR:766.0,460.1')] ).
cnf(778,plain,
( ~ member(skf2(intersection(u,v),intersection(u,w)),v)
| subset(intersection(u,w),intersection(u,v))
| subset(x,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[43,76]),
[iquote('0:Res:43.1,76.0')] ).
cnf(780,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)],[38,76]),
[iquote('0:Res:38.1,76.0')] ).
cnf(786,plain,
( ~ member(skf2(intersection(u,v),intersection(w,u)),v)
| subset(intersection(w,u),intersection(u,v)) ),
inference(con,[status(thm)],[780]),
[iquote('0:Con:780.2')] ).
cnf(788,plain,
( ~ member(skf2(intersection(u,v),intersection(u,w)),v)
| subset(intersection(u,w),intersection(u,v)) ),
inference(con,[status(thm)],[778]),
[iquote('0:Con:778.2')] ).
cnf(1005,plain,
( ~ member(skf3(intersection(skc4,u),v),skc3)
| ~ member(skf3(intersection(skc4,u),v),u)
| ~ member(skf3(intersection(skc4,u),v),v)
| equal(v,intersection(skc4,u)) ),
inference(res,[status(thm),theory(equality)],[3,119]),
[iquote('0:Res:3.1,119.0')] ).
cnf(3180,plain,
( equal(intersection(skc3,u),skc3)
| member(skf3(skc3,intersection(skc3,u)),skc5)
| equal(intersection(skc3,u),skc3) ),
inference(res,[status(thm),theory(equality)],[262,488]),
[iquote('0:Res:262.1,488.0')] ).
cnf(3183,plain,
( member(skf3(skc3,intersection(skc3,u)),skc5)
| equal(intersection(skc3,u),skc3) ),
inference(obv,[status(thm),theory(equality)],[3180]),
[iquote('0:Obv:3180.0')] ).
cnf(3198,plain,
( equal(intersection(skc3,skc5),skc3)
| equal(intersection(skc3,skc5),skc3) ),
inference(res,[status(thm),theory(equality)],[3183,771]),
[iquote('0:Res:3183.0,771.0')] ).
cnf(3199,plain,
equal(intersection(skc3,skc5),skc3),
inference(obv,[status(thm),theory(equality)],[3198]),
[iquote('0:Obv:3198.0')] ).
cnf(5244,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)],[148,786]),
[iquote('0:Res:148.1,786.0')] ).
cnf(5266,plain,
subset(intersection(intersection(u,v),w),intersection(w,v)),
inference(obv,[status(thm),theory(equality)],[5244]),
[iquote('0:Obv:5244.0')] ).
cnf(6869,plain,
subset(intersection(skc3,u),intersection(u,skc5)),
inference(spr,[status(thm),theory(equality)],[3199,5266]),
[iquote('0:SpR:3199.0,5266.0')] ).
cnf(8427,plain,
( subset(intersection(skc4,skc5),u)
| subset(intersection(skc4,skc5),u)
| member(skf2(u,intersection(skc4,skc5)),skc3) ),
inference(res,[status(thm),theory(equality)],[43,126]),
[iquote('0:Res:43.1,126.0')] ).
cnf(8440,plain,
( subset(intersection(skc4,skc5),u)
| member(skf2(u,intersection(skc4,skc5)),skc3) ),
inference(obv,[status(thm),theory(equality)],[8427]),
[iquote('0:Obv:8427.0')] ).
cnf(24469,plain,
( ~ member(skf3(intersection(skc4,skc3),skc3),skc3)
| ~ member(skf3(intersection(skc4,skc3),skc3),skc3)
| equal(intersection(skc4,skc3),skc3)
| equal(intersection(skc4,skc3),skc3) ),
inference(res,[status(thm),theory(equality)],[410,1005]),
[iquote('0:Res:410.1,1005.0')] ).
cnf(24482,plain,
( ~ member(skf3(intersection(skc4,skc3),skc3),skc3)
| equal(intersection(skc4,skc3),skc3) ),
inference(obv,[status(thm),theory(equality)],[24469]),
[iquote('0:Obv:24469.2')] ).
cnf(24483,plain,
( ~ member(skf3(intersection(skc3,skc4),skc3),skc3)
| equal(intersection(skc3,skc4),skc3) ),
inference(rew,[status(thm),theory(equality)],[7,24482]),
[iquote('0:Rew:7.0,24482.1,7.0,24482.0')] ).
cnf(24484,plain,
equal(intersection(skc3,skc4),skc3),
inference(mrr,[status(thm)],[24483,348]),
[iquote('0:MRR:24483.0,348.1')] ).
cnf(24635,plain,
subset(skc3,intersection(skc4,skc5)),
inference(spr,[status(thm),theory(equality)],[24484,6869]),
[iquote('0:SpR:24484.0,6869.0')] ).
cnf(24837,plain,
~ subset(intersection(skc4,skc5),skc3),
inference(mrr,[status(thm)],[20,24635]),
[iquote('0:MRR:20.0,24635.0')] ).
cnf(28498,plain,
( subset(intersection(skc4,skc5),intersection(skc4,skc3))
| subset(intersection(skc4,skc5),intersection(skc4,skc3)) ),
inference(res,[status(thm),theory(equality)],[8440,788]),
[iquote('0:Res:8440.1,788.0')] ).
cnf(28512,plain,
subset(intersection(skc4,skc5),intersection(skc4,skc3)),
inference(obv,[status(thm),theory(equality)],[28498]),
[iquote('0:Obv:28498.0')] ).
cnf(28513,plain,
subset(intersection(skc4,skc5),skc3),
inference(rew,[status(thm),theory(equality)],[24484,28512,7]),
[iquote('0:Rew:24484.0,28512.0,7.0,28512.0')] ).
cnf(28514,plain,
$false,
inference(mrr,[status(thm)],[28513,24837]),
[iquote('0:MRR:28513.0,24837.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 05:19:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 7.29/7.45
% 7.29/7.45 SPASS V 3.9
% 7.29/7.45 SPASS beiseite: Proof found.
% 7.29/7.45 % SZS status Theorem
% 7.29/7.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.29/7.45 SPASS derived 22445 clauses, backtracked 315 clauses, performed 3 splits and kept 4208 clauses.
% 7.29/7.45 SPASS allocated 102307 KBytes.
% 7.29/7.45 SPASS spent 0:00:06.88 on the problem.
% 7.29/7.45 0:00:00.04 for the input.
% 7.29/7.45 0:00:00.03 for the FLOTTER CNF translation.
% 7.29/7.45 0:00:00.21 for inferences.
% 7.29/7.45 0:00:00.20 for the backtracking.
% 7.29/7.45 0:00:06.34 for the reduction.
% 7.29/7.45
% 7.29/7.45
% 7.29/7.45 Here is a proof with depth 7, length 60 :
% 7.29/7.45 % SZS output start Refutation
% See solution above
% 7.29/7.45 Formulae used in the proof : prove_th19 commutativity_of_intersection subset_defn intersection_defn equal_defn equal_member_defn
% 7.29/7.45
%------------------------------------------------------------------------------