TSTP Solution File: SET639+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:27:46 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 8 unt; 0 nHn; 9 RR)
% Number of literals : 10 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc2,skc3),
file('SET639+3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(skc2,empty_set),
file('SET639+3.p',unknown),
[] ).
cnf(5,axiom,
equal(intersection(skc3,skc2),empty_set),
file('SET639+3.p',unknown),
[] ).
cnf(9,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET639+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ subset(u,v)
| equal(intersection(u,v),u) ),
file('SET639+3.p',unknown),
[] ).
cnf(23,plain,
equal(intersection(skc2,skc3),empty_set),
inference(rew,[status(thm),theory(equality)],[9,5]),
[iquote('0:Rew:9.0,5.0')] ).
cnf(27,plain,
equal(intersection(skc2,skc3),skc2),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(38,plain,
equal(skc2,empty_set),
inference(rew,[status(thm),theory(equality)],[23,27]),
[iquote('0:Rew:23.0,27.0')] ).
cnf(39,plain,
$false,
inference(mrr,[status(thm)],[38,3]),
[iquote('0:MRR:38.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 : Sat Jul 9 21:14:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 22 clauses.
% 0.18/0.43 SPASS allocated 97847 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 1, length 9 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : prove_th121 commutativity_of_intersection subset_intersection
% 0.18/0.43
%------------------------------------------------------------------------------