TSTP Solution File: SET005-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 05:22:21 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 52 ( 15 unt; 7 nHn; 52 RR)
% Number of literals : 105 ( 0 equ; 51 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
intersection(a,b,aIb),
file('SET005-1.p',unknown),
[] ).
cnf(2,axiom,
intersection(b,c,bIc),
file('SET005-1.p',unknown),
[] ).
cnf(3,axiom,
intersection(a,bIc,aIbIc),
file('SET005-1.p',unknown),
[] ).
cnf(4,axiom,
~ intersection(aIb,c,aIbIc),
file('SET005-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(u,v)
| ~ member(w,u)
| member(w,v) ),
file('SET005-1.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| member(member_of_1_not_of_2(u,v),u) ),
file('SET005-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(member_of_1_not_of_2(u,v),v)
| subset(u,v) ),
file('SET005-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,v)
| ~ intersection(w,x,v)
| member(u,w) ),
file('SET005-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,v)
| ~ intersection(w,x,v)
| member(u,x) ),
file('SET005-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,v)
| ~ member(u,w)
| ~ intersection(v,w,x)
| member(u,x) ),
file('SET005-1.p',unknown),
[] ).
cnf(14,axiom,
( member(h(u,v,w),u)
| member(h(u,v,w),w)
| intersection(u,v,w) ),
file('SET005-1.p',unknown),
[] ).
cnf(15,axiom,
( member(h(u,v,w),v)
| member(h(u,v,w),w)
| intersection(u,v,w) ),
file('SET005-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(h(u,v,w),u)
| ~ member(h(u,v,w),v)
| ~ member(h(u,v,w),w)
| intersection(u,v,w) ),
file('SET005-1.p',unknown),
[] ).
cnf(17,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),c)
| ~ member(h(aIb,c,aIbIc),aIbIc) ),
inference(res,[status(thm),theory(equality)],[16,4]),
[iquote('0:Res:16.3,4.0')] ).
cnf(18,plain,
( member(h(aIb,c,aIbIc),aIb)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(res,[status(thm),theory(equality)],[14,4]),
[iquote('0:Res:14.1,4.0')] ).
cnf(19,plain,
( member(h(aIb,c,aIbIc),c)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(res,[status(thm),theory(equality)],[15,4]),
[iquote('0:Res:15.1,4.0')] ).
cnf(20,plain,
member(h(aIb,c,aIbIc),aIbIc),
inference(spt,[spt(split,[position(s1)])],[19]),
[iquote('1:Spt:19.1')] ).
cnf(21,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),c) ),
inference(mrr,[status(thm)],[17,20]),
[iquote('1:MRR:17.2,20.0')] ).
cnf(27,plain,
( ~ member(u,aIbIc)
| member(u,bIc) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.0,12.1')] ).
cnf(28,plain,
( ~ member(u,aIb)
| member(u,b) ),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.1')] ).
cnf(29,plain,
( ~ member(u,bIc)
| member(u,c) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.1')] ).
cnf(32,plain,
( ~ member(u,aIbIc)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.0,11.1')] ).
cnf(33,plain,
( ~ member(u,aIb)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.1')] ).
cnf(34,plain,
( ~ member(u,bIc)
| member(u,b) ),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.1')] ).
cnf(35,plain,
( ~ member(member_of_1_not_of_2(u,c),bIc)
| subset(u,c) ),
inference(res,[status(thm),theory(equality)],[29,7]),
[iquote('0:Res:29.1,7.0')] ).
cnf(38,plain,
( ~ member(member_of_1_not_of_2(u,b),bIc)
| subset(u,b) ),
inference(res,[status(thm),theory(equality)],[34,7]),
[iquote('0:Res:34.1,7.0')] ).
cnf(39,plain,
( ~ member(u,a)
| ~ member(u,bIc)
| member(u,aIbIc) ),
inference(res,[status(thm),theory(equality)],[3,13]),
[iquote('0:Res:3.0,13.2')] ).
cnf(40,plain,
( ~ member(u,a)
| ~ member(u,b)
| member(u,aIb) ),
inference(res,[status(thm),theory(equality)],[1,13]),
[iquote('0:Res:1.0,13.2')] ).
cnf(41,plain,
( ~ member(u,b)
| ~ member(u,c)
| member(u,bIc) ),
inference(res,[status(thm),theory(equality)],[2,13]),
[iquote('0:Res:2.0,13.2')] ).
cnf(50,plain,
( ~ member(member_of_1_not_of_2(u,c),aIbIc)
| subset(u,c) ),
inference(res,[status(thm),theory(equality)],[27,35]),
[iquote('0:Res:27.1,35.0')] ).
cnf(61,plain,
( ~ member(member_of_1_not_of_2(u,b),aIbIc)
| subset(u,b) ),
inference(res,[status(thm),theory(equality)],[27,38]),
[iquote('0:Res:27.1,38.0')] ).
cnf(73,plain,
( subset(aIbIc,c)
| subset(aIbIc,c) ),
inference(res,[status(thm),theory(equality)],[6,50]),
[iquote('0:Res:6.1,50.0')] ).
cnf(74,plain,
subset(aIbIc,c),
inference(obv,[status(thm),theory(equality)],[73]),
[iquote('0:Obv:73.0')] ).
cnf(75,plain,
( ~ member(u,aIbIc)
| member(u,c) ),
inference(res,[status(thm),theory(equality)],[74,5]),
[iquote('0:Res:74.0,5.0')] ).
cnf(78,plain,
( subset(aIbIc,b)
| subset(aIbIc,b) ),
inference(res,[status(thm),theory(equality)],[6,61]),
[iquote('0:Res:6.1,61.0')] ).
cnf(79,plain,
subset(aIbIc,b),
inference(obv,[status(thm),theory(equality)],[78]),
[iquote('0:Obv:78.0')] ).
cnf(83,plain,
( ~ member(u,aIbIc)
| member(u,b) ),
inference(res,[status(thm),theory(equality)],[79,5]),
[iquote('0:Res:79.0,5.0')] ).
cnf(99,plain,
( ~ member(u,aIb)
| ~ member(u,bIc)
| member(u,aIbIc) ),
inference(res,[status(thm),theory(equality)],[33,39]),
[iquote('0:Res:33.1,39.0')] ).
cnf(109,plain,
( ~ member(u,aIbIc)
| ~ member(u,b)
| member(u,aIb) ),
inference(res,[status(thm),theory(equality)],[32,40]),
[iquote('0:Res:32.1,40.0')] ).
cnf(110,plain,
( ~ member(u,aIbIc)
| member(u,aIb) ),
inference(mrr,[status(thm)],[109,83]),
[iquote('0:MRR:109.1,83.1')] ).
cnf(127,plain,
( ~ member(u,aIb)
| ~ member(u,c)
| member(u,bIc) ),
inference(res,[status(thm),theory(equality)],[28,41]),
[iquote('0:Res:28.1,41.0')] ).
cnf(162,plain,
( ~ member(h(aIb,c,aIbIc),aIbIc)
| ~ member(h(aIb,c,aIbIc),c) ),
inference(res,[status(thm),theory(equality)],[110,21]),
[iquote('1:Res:110.1,21.0')] ).
cnf(163,plain,
~ member(h(aIb,c,aIbIc),c),
inference(mrr,[status(thm)],[162,20]),
[iquote('1:MRR:162.0,20.0')] ).
cnf(168,plain,
~ member(h(aIb,c,aIbIc),aIbIc),
inference(res,[status(thm),theory(equality)],[75,163]),
[iquote('1:Res:75.1,163.0')] ).
cnf(170,plain,
$false,
inference(mrr,[status(thm)],[168,20]),
[iquote('1:MRR:168.0,20.0')] ).
cnf(171,plain,
~ member(h(aIb,c,aIbIc),aIbIc),
inference(spt,[spt(split,[position(sa)])],[170,20]),
[iquote('1:Spt:170.0,19.1,20.0')] ).
cnf(172,plain,
member(h(aIb,c,aIbIc),c),
inference(spt,[spt(split,[position(s2)])],[19]),
[iquote('1:Spt:170.0,19.0')] ).
cnf(173,plain,
member(h(aIb,c,aIbIc),aIb),
inference(mrr,[status(thm)],[18,110]),
[iquote('0:MRR:18.1,110.0')] ).
cnf(175,plain,
( ~ member(h(aIb,c,aIbIc),c)
| member(h(aIb,c,aIbIc),bIc) ),
inference(res,[status(thm),theory(equality)],[173,127]),
[iquote('0:Res:173.0,127.0')] ).
cnf(176,plain,
( ~ member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(res,[status(thm),theory(equality)],[173,99]),
[iquote('0:Res:173.0,99.0')] ).
cnf(177,plain,
member(h(aIb,c,aIbIc),bIc),
inference(mrr,[status(thm)],[175,172]),
[iquote('1:MRR:175.0,172.0')] ).
cnf(178,plain,
$false,
inference(mrr,[status(thm)],[176,177,171]),
[iquote('1:MRR:176.0,176.1,177.0,171.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.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 12:59:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 136 clauses, backtracked 4 clauses, performed 1 splits and kept 120 clauses.
% 0.20/0.42 SPASS allocated 63229 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.01 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 6, length 52 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : a_intersection_b b_intersection_c a_intersection_bIc prove_aIb_intersection_c_is_aIbIc membership_in_subsets subsets_axiom1 subsets_axiom2 member_of_intersection_is_member_of_set1 member_of_intersection_is_member_of_set2 member_of_both_is_member_of_intersection intersection_axiom1 intersection_axiom2 intersection_axiom3
% 0.20/0.42
%------------------------------------------------------------------------------