TSTP Solution File: SET001-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 05:22:18 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 0 nHn; 9 RR)
% Number of literals : 14 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal_sets(b,bb),
file('SET001-1.p',unknown),
[] ).
cnf(2,axiom,
member(element_of_b,b),
file('SET001-1.p',unknown),
[] ).
cnf(3,axiom,
~ member(element_of_b,bb),
file('SET001-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ subset(u,v)
| ~ member(w,u)
| member(w,v) ),
file('SET001-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal_sets(u,v)
| subset(u,v) ),
file('SET001-1.p',unknown),
[] ).
cnf(10,plain,
( ~ subset(u,bb)
| ~ member(element_of_b,u) ),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.2,3.0')] ).
cnf(12,plain,
( ~ equal_sets(u,bb)
| ~ member(element_of_b,u) ),
inference(res,[status(thm),theory(equality)],[7,10]),
[iquote('0:Res:7.1,10.0')] ).
cnf(14,plain,
~ equal_sets(b,bb),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.1')] ).
cnf(15,plain,
$false,
inference(mrr,[status(thm)],[14,1]),
[iquote('0:MRR:14.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n020.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 : Mon Jul 11 02:48:58 EDT 2022
% 0.14/0.34 % 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 5 clauses, backtracked 0 clauses, performed 0 splits and kept 14 clauses.
% 0.20/0.41 SPASS allocated 63084 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 3, length 9 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : b_equals_bb element_of_b prove_element_of_bb membership_in_subsets set_equal_sets_are_subsets1
% 0.20/0.41
%------------------------------------------------------------------------------