%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 05:22:22 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 12 unt; 11 nHn; 50 RR)
% Number of literals : 117 ( 0 equ; 59 neg)
% Maximal clause size : 5 ( 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; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
union(b,c,bUc),
file('SET007-1.p',unknown),
[] ).
cnf(2,axiom,
intersection(a,b,aIb),
file('SET007-1.p',unknown),
[] ).
cnf(3,axiom,
intersection(a,c,aIc),
file('SET007-1.p',unknown),
[] ).
cnf(4,axiom,
intersection(a,bUc,aI_bUc),
file('SET007-1.p',unknown),
[] ).
cnf(5,axiom,
~ union(aIb,aIc,aI_bUc),
file('SET007-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,v)
| ~ union(w,x,v)
| member(u,x)
| member(u,w) ),
file('SET007-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,v)
| ~ union(v,w,x)
| member(u,x) ),
file('SET007-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| ~ union(w,v,x)
| member(u,x) ),
file('SET007-1.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('SET007-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(g(u,v,w),w)
| ~ member(g(u,v,w),u)
| union(u,v,w) ),
file('SET007-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(g(u,v,w),w)
| ~ member(g(u,v,w),v)
| union(u,v,w) ),
file('SET007-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(u,v)
| ~ intersection(w,x,v)
| member(u,w) ),
file('SET007-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,v)
| ~ intersection(w,x,v)
| member(u,x) ),
file('SET007-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ member(u,v)
| ~ member(u,w)
| ~ intersection(v,w,x)
| member(u,x) ),
file('SET007-1.p',unknown),
[] ).
cnf(24,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aIb) ),
inference(res,[status(thm),theory(equality)],[15,5]),
[iquote('0:Res:15.0,5.0')] ).
cnf(25,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(res,[status(thm),theory(equality)],[16,5]),
[iquote('0:Res:16.2,5.0')] ).
cnf(26,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(res,[status(thm),theory(equality)],[17,5]),
[iquote('0:Res:17.2,5.0')] ).
cnf(27,plain,
member(g(aIb,aIc,aI_bUc),aI_bUc),
inference(spt,[spt(split,[position(s1)])],[24]),
[iquote('1:Spt:24.0')] ).
cnf(28,plain,
~ member(g(aIb,aIc,aI_bUc),aIc),
inference(mrr,[status(thm)],[26,27]),
[iquote('1:MRR:26.0,27.0')] ).
cnf(29,plain,
~ member(g(aIb,aIc,aI_bUc),aIb),
inference(mrr,[status(thm)],[25,27]),
[iquote('1:MRR:25.0,27.0')] ).
cnf(35,plain,
( ~ member(u,c)
| member(u,bUc) ),
inference(res,[status(thm),theory(equality)],[1,14]),
[iquote('0:Res:1.0,14.1')] ).
cnf(40,plain,
( ~ member(u,b)
| member(u,bUc) ),
inference(res,[status(thm),theory(equality)],[1,13]),
[iquote('0:Res:1.0,13.1')] ).
cnf(41,plain,
( ~ member(u,aI_bUc)
| member(u,bUc) ),
inference(res,[status(thm),theory(equality)],[4,19]),
[iquote('0:Res:4.0,19.1')] ).
cnf(42,plain,
( ~ member(u,aIc)
| member(u,c) ),
inference(res,[status(thm),theory(equality)],[3,19]),
[iquote('0:Res:3.0,19.1')] ).
cnf(43,plain,
( ~ member(u,aIb)
| member(u,b) ),
inference(res,[status(thm),theory(equality)],[2,19]),
[iquote('0:Res:2.0,19.1')] ).
cnf(47,plain,
( ~ member(u,aIc)
| member(u,bUc) ),
inference(res,[status(thm),theory(equality)],[42,35]),
[iquote('0:Res:42.1,35.0')] ).
cnf(49,plain,
( ~ member(u,aIb)
| member(u,bUc) ),
inference(res,[status(thm),theory(equality)],[43,40]),
[iquote('0:Res:43.1,40.0')] ).
cnf(50,plain,
( ~ member(u,aI_bUc)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[4,18]),
[iquote('0:Res:4.0,18.1')] ).
cnf(51,plain,
( ~ member(u,aIc)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[3,18]),
[iquote('0:Res:3.0,18.1')] ).
cnf(52,plain,
( ~ member(u,aIb)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.1')] ).
cnf(57,plain,
( ~ member(u,bUc)
| member(u,c)
| member(u,b) ),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.1')] ).
cnf(64,plain,
( ~ member(u,a)
| ~ member(u,bUc)
| member(u,aI_bUc) ),
inference(res,[status(thm),theory(equality)],[4,20]),
[iquote('0:Res:4.0,20.2')] ).
cnf(65,plain,
( ~ member(u,a)
| ~ member(u,c)
| member(u,aIc) ),
inference(res,[status(thm),theory(equality)],[3,20]),
[iquote('0:Res:3.0,20.2')] ).
cnf(66,plain,
( ~ member(u,a)
| ~ member(u,b)
| member(u,aIb) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.2')] ).
cnf(143,plain,
( ~ member(u,aIb)
| ~ member(u,a)
| member(u,aI_bUc) ),
inference(res,[status(thm),theory(equality)],[49,64]),
[iquote('0:Res:49.1,64.1')] ).
cnf(144,plain,
( ~ member(u,aIc)
| ~ member(u,a)
| member(u,aI_bUc) ),
inference(res,[status(thm),theory(equality)],[47,64]),
[iquote('0:Res:47.1,64.1')] ).
cnf(156,plain,
( ~ member(u,aIb)
| member(u,aI_bUc) ),
inference(mrr,[status(thm)],[143,52]),
[iquote('0:MRR:143.1,52.1')] ).
cnf(157,plain,
( ~ member(u,aIc)
| member(u,aI_bUc) ),
inference(mrr,[status(thm)],[144,51]),
[iquote('0:MRR:144.1,51.1')] ).
cnf(239,plain,
( ~ member(u,bUc)
| ~ member(u,a)
| member(u,c)
| member(u,aIb) ),
inference(res,[status(thm),theory(equality)],[57,66]),
[iquote('0:Res:57.2,66.1')] ).
cnf(478,plain,
( ~ member(u,bUc)
| ~ member(u,a)
| ~ member(u,a)
| member(u,aIb)
| member(u,aIc) ),
inference(res,[status(thm),theory(equality)],[239,65]),
[iquote('0:Res:239.2,65.1')] ).
cnf(482,plain,
( ~ member(u,bUc)
| ~ member(u,a)
| member(u,aIb)
| member(u,aIc) ),
inference(obv,[status(thm),theory(equality)],[478]),
[iquote('0:Obv:478.1')] ).
cnf(949,plain,
( ~ member(u,aI_bUc)
| ~ member(u,a)
| member(u,aIb)
| member(u,aIc) ),
inference(res,[status(thm),theory(equality)],[41,482]),
[iquote('0:Res:41.1,482.0')] ).
cnf(981,plain,
( ~ member(u,aI_bUc)
| member(u,aIb)
| member(u,aIc) ),
inference(mrr,[status(thm)],[949,50]),
[iquote('0:MRR:949.1,50.1')] ).
cnf(997,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(res,[status(thm),theory(equality)],[981,29]),
[iquote('1:Res:981.1,29.0')] ).
cnf(1013,plain,
$false,
inference(mrr,[status(thm)],[997,27,28]),
[iquote('1:MRR:997.0,997.1,27.0,28.0')] ).
cnf(1015,plain,
~ member(g(aIb,aIc,aI_bUc),aI_bUc),
inference(spt,[spt(split,[position(sa)])],[1013,27]),
[iquote('1:Spt:1013.0,24.0,27.0')] ).
cnf(1016,plain,
( member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aIb) ),
inference(spt,[spt(split,[position(s2)])],[24]),
[iquote('1:Spt:1013.0,24.1,24.2')] ).
cnf(1017,plain,
( member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(res,[status(thm),theory(equality)],[1016,156]),
[iquote('1:Res:1016.1,156.0')] ).
cnf(1018,plain,
member(g(aIb,aIc,aI_bUc),aI_bUc),
inference(mrr,[status(thm)],[1017,157]),
[iquote('1:MRR:1017.0,157.0')] ).
cnf(1019,plain,
$false,
inference(mrr,[status(thm)],[1018,1015]),
[iquote('1:MRR:1018.0,1015.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 00:30:30 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 795 clauses, backtracked 52 clauses, performed 3 splits and kept 496 clauses.
% 0.20/0.50 SPASS allocated 63941 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.06 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 5, length 50 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : b_union_c a_intersection_b a_intersection_c a_intersection_bUc prove_aIb_union_aIc_is_aI_bUc member_of_union_is_member_of_one_set member_of_set1_is_member_of_union member_of_set2_is_member_of_union 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
% 0.20/0.50
%------------------------------------------------------------------------------