TSTP Solution File: SET010-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 05:22:24 EDT 2022
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 12 unt; 13 nHn; 50 RR)
% Number of literals : 117 ( 0 equ; 61 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
intersection(a,b,aIb),
file('SET010-1.p',unknown),
[] ).
cnf(2,axiom,
difference(c,a,cDa),
file('SET010-1.p',unknown),
[] ).
cnf(3,axiom,
difference(c,b,cDb),
file('SET010-1.p',unknown),
[] ).
cnf(4,axiom,
difference(c,aIb,cD_aIb),
file('SET010-1.p',unknown),
[] ).
cnf(5,axiom,
~ union(cDa,cDb,cD_aIb),
file('SET010-1.p',unknown),
[] ).
cnf(15,axiom,
( member(g(u,v,w),w)
| member(g(u,v,w),v)
| member(g(u,v,w),u)
| union(u,v,w) ),
file('SET010-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(g(u,v,w),w)
| ~ member(g(u,v,w),u)
| union(u,v,w) ),
file('SET010-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(g(u,v,w),w)
| ~ member(g(u,v,w),v)
| union(u,v,w) ),
file('SET010-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(u,v)
| ~ intersection(w,x,v)
| member(u,w) ),
file('SET010-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,v)
| ~ intersection(w,x,v)
| member(u,x) ),
file('SET010-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ member(u,v)
| ~ member(u,w)
| ~ intersection(v,w,x)
| member(u,x) ),
file('SET010-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ difference(w,x,v)
| member(u,w) ),
file('SET010-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,w)
| ~ difference(x,w,v) ),
file('SET010-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ difference(v,w,x)
| member(u,w)
| member(u,x) ),
file('SET010-1.p',unknown),
[] ).
cnf(30,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(res,[status(thm),theory(equality)],[15,5]),
[iquote('0:Res:15.0,5.0')] ).
cnf(31,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(res,[status(thm),theory(equality)],[16,5]),
[iquote('0:Res:16.2,5.0')] ).
cnf(32,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDb) ),
inference(res,[status(thm),theory(equality)],[17,5]),
[iquote('0:Res:17.2,5.0')] ).
cnf(33,plain,
member(g(cDa,cDb,cD_aIb),cD_aIb),
inference(spt,[spt(split,[position(s1)])],[30]),
[iquote('1:Spt:30.0')] ).
cnf(34,plain,
~ member(g(cDa,cDb,cD_aIb),cDb),
inference(mrr,[status(thm)],[32,33]),
[iquote('1:MRR:32.0,33.0')] ).
cnf(35,plain,
~ member(g(cDa,cDb,cD_aIb),cDa),
inference(mrr,[status(thm)],[31,33]),
[iquote('1:MRR:31.0,33.0')] ).
cnf(41,plain,
( ~ member(u,aIb)
| member(u,b) ),
inference(res,[status(thm),theory(equality)],[1,19]),
[iquote('0:Res:1.0,19.1')] ).
cnf(46,plain,
( ~ member(u,aIb)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.1')] ).
cnf(51,plain,
( ~ member(u,cD_aIb)
| member(u,c) ),
inference(res,[status(thm),theory(equality)],[4,24]),
[iquote('0:Res:4.0,24.1')] ).
cnf(52,plain,
( ~ member(u,cDb)
| member(u,c) ),
inference(res,[status(thm),theory(equality)],[3,24]),
[iquote('0:Res:3.0,24.1')] ).
cnf(53,plain,
( ~ member(u,cDa)
| member(u,c) ),
inference(res,[status(thm),theory(equality)],[2,24]),
[iquote('0:Res:2.0,24.1')] ).
cnf(59,plain,
( ~ member(u,cD_aIb)
| ~ member(u,aIb) ),
inference(res,[status(thm),theory(equality)],[4,25]),
[iquote('0:Res:4.0,25.2')] ).
cnf(60,plain,
( ~ member(u,cDb)
| ~ member(u,b) ),
inference(res,[status(thm),theory(equality)],[3,25]),
[iquote('0:Res:3.0,25.2')] ).
cnf(61,plain,
( ~ member(u,cDa)
| ~ member(u,a) ),
inference(res,[status(thm),theory(equality)],[2,25]),
[iquote('0:Res:2.0,25.2')] ).
cnf(65,plain,
( ~ member(u,aIb)
| ~ member(u,cDb) ),
inference(res,[status(thm),theory(equality)],[41,60]),
[iquote('0:Res:41.1,60.1')] ).
cnf(67,plain,
( ~ member(u,aIb)
| ~ member(u,cDa) ),
inference(res,[status(thm),theory(equality)],[46,61]),
[iquote('0:Res:46.1,61.1')] ).
cnf(73,plain,
( ~ member(u,c)
| member(u,aIb)
| member(u,cD_aIb) ),
inference(res,[status(thm),theory(equality)],[4,26]),
[iquote('0:Res:4.0,26.1')] ).
cnf(74,plain,
( ~ member(u,c)
| member(u,b)
| member(u,cDb) ),
inference(res,[status(thm),theory(equality)],[3,26]),
[iquote('0:Res:3.0,26.1')] ).
cnf(75,plain,
( ~ member(u,c)
| member(u,a)
| member(u,cDa) ),
inference(res,[status(thm),theory(equality)],[2,26]),
[iquote('0:Res:2.0,26.1')] ).
cnf(79,plain,
( ~ member(u,a)
| ~ member(u,b)
| member(u,aIb) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.2')] ).
cnf(83,plain,
( ~ member(u,c)
| ~ member(u,cDa)
| member(u,cD_aIb) ),
inference(res,[status(thm),theory(equality)],[73,67]),
[iquote('0:Res:73.1,67.0')] ).
cnf(84,plain,
( ~ member(u,c)
| ~ member(u,cDb)
| member(u,cD_aIb) ),
inference(res,[status(thm),theory(equality)],[73,65]),
[iquote('0:Res:73.1,65.0')] ).
cnf(86,plain,
( ~ member(u,cDa)
| member(u,cD_aIb) ),
inference(mrr,[status(thm)],[83,53]),
[iquote('0:MRR:83.0,53.1')] ).
cnf(87,plain,
( ~ member(u,cDb)
| member(u,cD_aIb) ),
inference(mrr,[status(thm)],[84,52]),
[iquote('0:MRR:84.0,52.1')] ).
cnf(311,plain,
( ~ member(u,c)
| ~ member(u,b)
| member(u,cDa)
| member(u,aIb) ),
inference(res,[status(thm),theory(equality)],[75,79]),
[iquote('0:Res:75.1,79.0')] ).
cnf(555,plain,
( ~ member(u,c)
| ~ member(u,c)
| member(u,cDb)
| member(u,cDa)
| member(u,aIb) ),
inference(res,[status(thm),theory(equality)],[74,311]),
[iquote('0:Res:74.1,311.1')] ).
cnf(568,plain,
( ~ member(u,c)
| member(u,cDb)
| member(u,cDa)
| member(u,aIb) ),
inference(obv,[status(thm),theory(equality)],[555]),
[iquote('0:Obv:555.0')] ).
cnf(618,plain,
( ~ member(u,c)
| ~ member(u,cD_aIb)
| member(u,cDb)
| member(u,cDa) ),
inference(res,[status(thm),theory(equality)],[568,59]),
[iquote('0:Res:568.3,59.1')] ).
cnf(625,plain,
( ~ member(u,cD_aIb)
| member(u,cDb)
| member(u,cDa) ),
inference(mrr,[status(thm)],[618,51]),
[iquote('0:MRR:618.0,51.1')] ).
cnf(626,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(res,[status(thm),theory(equality)],[625,35]),
[iquote('1:Res:625.2,35.0')] ).
cnf(653,plain,
$false,
inference(mrr,[status(thm)],[626,33,34]),
[iquote('1:MRR:626.0,626.1,33.0,34.0')] ).
cnf(654,plain,
~ member(g(cDa,cDb,cD_aIb),cD_aIb),
inference(spt,[spt(split,[position(sa)])],[653,33]),
[iquote('1:Spt:653.0,30.0,33.0')] ).
cnf(655,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(spt,[spt(split,[position(s2)])],[30]),
[iquote('1:Spt:653.0,30.1,30.2')] ).
cnf(656,plain,
( member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(res,[status(thm),theory(equality)],[655,86]),
[iquote('1:Res:655.1,86.0')] ).
cnf(657,plain,
member(g(cDa,cDb,cD_aIb),cD_aIb),
inference(mrr,[status(thm)],[656,87]),
[iquote('1:MRR:656.0,87.0')] ).
cnf(658,plain,
$false,
inference(mrr,[status(thm)],[657,654]),
[iquote('1:MRR:657.0,654.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 15:03:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47
% 0.18/0.47 SPASS V 3.9
% 0.18/0.47 SPASS beiseite: Proof found.
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 537 clauses, backtracked 4 clauses, performed 1 splits and kept 401 clauses.
% 0.18/0.47 SPASS allocated 63696 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.18/0.47 0:00:00.04 for the input.
% 0.18/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.47 0:00:00.01 for inferences.
% 0.18/0.47 0:00:00.00 for the backtracking.
% 0.18/0.47 0:00:00.05 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 5, length 50 :
% 0.18/0.47 % SZS output start Refutation
% See solution above
% 0.18/0.47 Formulae used in the proof : a_intersection_b c_minus_a c_minus_b c_minus_aIb prove_cDa_union_cDb_is_cD_aIb union_axiom1 union_axiom2 union_axiom3 member_of_intersection_is_member_of_set1 member_of_intersection_is_member_of_set2 member_of_both_is_member_of_intersection member_of_difference not_member_of_difference member_of_difference_or_set2
% 0.18/0.47
%------------------------------------------------------------------------------