TSTP Solution File: SET590+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET590+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:27:11 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 4 unt; 2 nHn; 8 RR)
% Number of literals : 12 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ subset(difference(skc3,skc2),skc3),
file('SET590+3.p',unknown),
[] ).
cnf(3,axiom,
( subset(u,v)
| member(skf1(v,u),u) ),
file('SET590+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,difference(v,w))
| member(u,v) ),
file('SET590+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(skf1(u,v),u)
| subset(w,u) ),
file('SET590+3.p',unknown),
[] ).
cnf(10,plain,
~ member(skf1(skc3,u),skc3),
inference(res,[status(thm),theory(equality)],[5,2]),
[iquote('0:Res:5.1,2.0')] ).
cnf(14,plain,
( subset(difference(u,v),w)
| member(skf1(w,difference(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[3,4]),
[iquote('0:Res:3.1,4.0')] ).
cnf(21,plain,
subset(difference(skc3,u),skc3),
inference(res,[status(thm),theory(equality)],[14,10]),
[iquote('0:Res:14.1,10.0')] ).
cnf(26,plain,
$false,
inference(unc,[status(thm)],[21,2]),
[iquote('0:UnC:21.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET590+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 23:07:22 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 19 clauses.
% 0.18/0.43 SPASS allocated 85157 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 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 2, length 8 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : prove_th49 subset_defn difference_defn
% 0.18/0.43
%------------------------------------------------------------------------------