%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 05:22:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 12 unt; 9 nHn; 31 RR)
% Number of literals : 62 ( 0 equ; 31 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 : 9 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
difference(a,b,aDb),
file('SET011-1.p',unknown),
[] ).
cnf(2,axiom,
difference(a,aDb,aD_aDb),
file('SET011-1.p',unknown),
[] ).
cnf(3,axiom,
~ intersection(a,b,aD_aDb),
file('SET011-1.p',unknown),
[] ).
cnf(13,axiom,
( member(h(u,v,w),u)
| member(h(u,v,w),w)
| intersection(u,v,w) ),
file('SET011-1.p',unknown),
[] ).
cnf(14,axiom,
( member(h(u,v,w),v)
| member(h(u,v,w),w)
| intersection(u,v,w) ),
file('SET011-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(h(u,v,w),u)
| ~ member(h(u,v,w),v)
| ~ member(h(u,v,w),w)
| intersection(u,v,w) ),
file('SET011-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(u,v)
| ~ difference(w,x,v)
| member(u,w) ),
file('SET011-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(u,v)
| ~ member(u,w)
| ~ difference(x,w,v) ),
file('SET011-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(u,v)
| ~ difference(v,w,x)
| member(u,w)
| member(u,x) ),
file('SET011-1.p',unknown),
[] ).
cnf(22,plain,
( ~ member(h(a,b,aD_aDb),a)
| ~ member(h(a,b,aD_aDb),b)
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(res,[status(thm),theory(equality)],[15,3]),
[iquote('0:Res:15.3,3.0')] ).
cnf(23,plain,
( member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(res,[status(thm),theory(equality)],[13,3]),
[iquote('0:Res:13.1,3.0')] ).
cnf(24,plain,
( member(h(a,b,aD_aDb),b)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(res,[status(thm),theory(equality)],[14,3]),
[iquote('0:Res:14.1,3.0')] ).
cnf(25,plain,
member(h(a,b,aD_aDb),aD_aDb),
inference(spt,[spt(split,[position(s1)])],[24]),
[iquote('1:Spt:24.1')] ).
cnf(26,plain,
( ~ member(h(a,b,aD_aDb),a)
| ~ member(h(a,b,aD_aDb),b) ),
inference(mrr,[status(thm)],[22,25]),
[iquote('1:MRR:22.2,25.0')] ).
cnf(32,plain,
( ~ member(u,aD_aDb)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[2,16]),
[iquote('0:Res:2.0,16.1')] ).
cnf(35,plain,
( ~ member(u,aD_aDb)
| ~ member(u,aDb) ),
inference(res,[status(thm),theory(equality)],[2,17]),
[iquote('0:Res:2.0,17.2')] ).
cnf(36,plain,
( ~ member(u,aDb)
| ~ member(u,b) ),
inference(res,[status(thm),theory(equality)],[1,17]),
[iquote('0:Res:1.0,17.2')] ).
cnf(42,plain,
( ~ member(u,a)
| member(u,aDb)
| member(u,aD_aDb) ),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.1')] ).
cnf(43,plain,
( ~ member(u,a)
| member(u,b)
| member(u,aDb) ),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.1')] ).
cnf(53,plain,
( ~ member(u,aD_aDb)
| member(u,b)
| member(u,aDb) ),
inference(res,[status(thm),theory(equality)],[32,43]),
[iquote('0:Res:32.1,43.0')] ).
cnf(54,plain,
( ~ member(u,aD_aDb)
| member(u,b) ),
inference(mrr,[status(thm)],[53,35]),
[iquote('0:MRR:53.2,35.1')] ).
cnf(176,plain,
( ~ member(h(a,b,aD_aDb),aD_aDb)
| ~ member(h(a,b,aD_aDb),b) ),
inference(res,[status(thm),theory(equality)],[32,26]),
[iquote('1:Res:32.1,26.0')] ).
cnf(177,plain,
~ member(h(a,b,aD_aDb),b),
inference(mrr,[status(thm)],[176,25]),
[iquote('1:MRR:176.0,25.0')] ).
cnf(182,plain,
~ member(h(a,b,aD_aDb),aD_aDb),
inference(res,[status(thm),theory(equality)],[54,177]),
[iquote('1:Res:54.1,177.0')] ).
cnf(183,plain,
$false,
inference(mrr,[status(thm)],[182,25]),
[iquote('1:MRR:182.0,25.0')] ).
cnf(184,plain,
~ member(h(a,b,aD_aDb),aD_aDb),
inference(spt,[spt(split,[position(sa)])],[183,25]),
[iquote('1:Spt:183.0,24.1,25.0')] ).
cnf(185,plain,
member(h(a,b,aD_aDb),b),
inference(spt,[spt(split,[position(s2)])],[24]),
[iquote('1:Spt:183.0,24.0')] ).
cnf(186,plain,
member(h(a,b,aD_aDb),a),
inference(mrr,[status(thm)],[23,32]),
[iquote('0:MRR:23.1,32.0')] ).
cnf(187,plain,
~ member(h(a,b,aD_aDb),aDb),
inference(res,[status(thm),theory(equality)],[185,36]),
[iquote('1:Res:185.0,36.1')] ).
cnf(190,plain,
( member(h(a,b,aD_aDb),aDb)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(res,[status(thm),theory(equality)],[186,42]),
[iquote('0:Res:186.0,42.0')] ).
cnf(191,plain,
$false,
inference(mrr,[status(thm)],[190,187,184]),
[iquote('1:MRR:190.0,190.1,187.0,184.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n025.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 00:06:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 140 clauses, backtracked 4 clauses, performed 1 splits and kept 119 clauses.
% 0.19/0.43 SPASS allocated 63253 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.01 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 3, length 31 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : a_minus_b a_minus_aDb prove_a_intersection_b_is_aD_aDb intersection_axiom1 intersection_axiom2 intersection_axiom3 member_of_difference not_member_of_difference member_of_difference_or_set2
% 0.19/0.43
%------------------------------------------------------------------------------