TSTP Solution File: SET009-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 05:22:23 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 8 unt; 4 nHn; 21 RR)
% Number of literals : 42 ( 0 equ; 21 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 : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(d,a),
file('SET009-1.p',unknown),
[] ).
cnf(2,axiom,
difference(b,a,bDa),
file('SET009-1.p',unknown),
[] ).
cnf(3,axiom,
difference(b,d,bDd),
file('SET009-1.p',unknown),
[] ).
cnf(4,axiom,
~ subset(bDa,bDd),
file('SET009-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(u,v)
| ~ member(w,u)
| member(w,v) ),
file('SET009-1.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| member(member_of_1_not_of_2(u,v),u) ),
file('SET009-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(member_of_1_not_of_2(u,v),v)
| subset(u,v) ),
file('SET009-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,v)
| ~ difference(w,x,v)
| member(u,w) ),
file('SET009-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,v)
| ~ member(u,w)
| ~ difference(x,w,v) ),
file('SET009-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,v)
| ~ difference(v,w,x)
| member(u,w)
| member(u,x) ),
file('SET009-1.p',unknown),
[] ).
cnf(18,plain,
~ member(member_of_1_not_of_2(bDa,bDd),bDd),
inference(res,[status(thm),theory(equality)],[7,4]),
[iquote('0:Res:7.1,4.0')] ).
cnf(19,plain,
member(member_of_1_not_of_2(bDa,bDd),bDa),
inference(res,[status(thm),theory(equality)],[6,4]),
[iquote('0:Res:6.0,4.0')] ).
cnf(27,plain,
( ~ member(u,d)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.0,5.0')] ).
cnf(33,plain,
( ~ member(u,bDa)
| member(u,b) ),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.1')] ).
cnf(36,plain,
( ~ member(u,bDa)
| ~ member(u,a) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.2')] ).
cnf(43,plain,
( ~ member(u,b)
| member(u,d)
| member(u,bDd) ),
inference(res,[status(thm),theory(equality)],[3,13]),
[iquote('0:Res:3.0,13.1')] ).
cnf(58,plain,
( ~ member(u,b)
| member(u,bDd)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[43,27]),
[iquote('0:Res:43.1,27.0')] ).
cnf(70,plain,
( ~ member(u,b)
| ~ member(u,bDa)
| member(u,bDd) ),
inference(res,[status(thm),theory(equality)],[58,36]),
[iquote('0:Res:58.2,36.1')] ).
cnf(72,plain,
( ~ member(u,bDa)
| member(u,bDd) ),
inference(mrr,[status(thm)],[70,33]),
[iquote('0:MRR:70.0,33.1')] ).
cnf(73,plain,
member(member_of_1_not_of_2(bDa,bDd),bDd),
inference(res,[status(thm),theory(equality)],[19,72]),
[iquote('0:Res:19.0,72.0')] ).
cnf(77,plain,
$false,
inference(mrr,[status(thm)],[73,18]),
[iquote('0:MRR:73.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 08:04:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 53 clauses, backtracked 0 clauses, performed 0 splits and kept 58 clauses.
% 0.20/0.41 SPASS allocated 63148 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.04 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 4, length 21 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : d_is_a_subset_of_a b_minus_a b_minus_d prove_bDa_is_a_subset_of_bDd membership_in_subsets subsets_axiom1 subsets_axiom2 member_of_difference not_member_of_difference member_of_difference_or_set2
% 0.20/0.41
%------------------------------------------------------------------------------