%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:28:07 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 6 unt; 2 nHn; 12 RR)
% Number of literals : 19 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ member(u,empty_set),
file('SET691+4.p',unknown),
[] ).
cnf(3,axiom,
( subset(skc1,empty_set)
| equal_set(skc1,empty_set) ),
file('SET691+4.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal_set(u,v)
| subset(u,v) ),
file('SET691+4.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset(skc1,empty_set)
| ~ equal_set(skc1,empty_set) ),
file('SET691+4.p',unknown),
[] ).
cnf(8,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET691+4.p',unknown),
[] ).
cnf(25,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal_set(v,u) ),
file('SET691+4.p',unknown),
[] ).
cnf(32,plain,
subset(skc1,empty_set),
inference(mrr,[status(thm)],[3,5]),
[iquote('0:MRR:3.1,5.0')] ).
cnf(33,plain,
~ equal_set(skc1,empty_set),
inference(mrr,[status(thm)],[7,32]),
[iquote('0:MRR:7.0,32.0')] ).
cnf(36,plain,
( ~ subset(empty_set,skc1)
| equal_set(skc1,empty_set) ),
inference(res,[status(thm),theory(equality)],[32,25]),
[iquote('0:Res:32.0,25.0')] ).
cnf(40,plain,
~ subset(empty_set,skc1),
inference(mrr,[status(thm)],[36,33]),
[iquote('0:MRR:36.1,33.0')] ).
cnf(44,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.1,1.0')] ).
cnf(48,plain,
$false,
inference(unc,[status(thm)],[44,40]),
[iquote('0:UnC:44.0,40.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 05:52:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.19/0.46 SPASS allocated 85401 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.00 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 1, length 12 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : empty_set thI16 equal_set subset
% 0.19/0.46
%------------------------------------------------------------------------------