%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU169+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:34:39 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 9 unt; 2 nHn; 18 RR)
% Number of literals : 31 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
in(skc7,skc6),
file('SEU169+1.p',unknown),
[] ).
cnf(6,axiom,
element(skc6,powerset(skc5)),
file('SEU169+1.p',unknown),
[] ).
cnf(7,axiom,
~ in(skc7,skc5),
file('SEU169+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU169+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU169+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ empty(u)
| ~ element(v,u)
| empty(v) ),
file('SEU169+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU169+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ in(u,v)
| ~ equal(v,powerset(w))
| subset(u,w) ),
file('SEU169+1.p',unknown),
[] ).
cnf(29,plain,
~ empty(skc6),
inference(res,[status(thm),theory(equality)],[3,13]),
[iquote('0:Res:3.0,13.1')] ).
cnf(35,plain,
( ~ subset(u,skc5)
| ~ in(skc7,u) ),
inference(res,[status(thm),theory(equality)],[22,7]),
[iquote('0:Res:22.2,7.0')] ).
cnf(37,plain,
( ~ empty(powerset(skc5))
| empty(skc6) ),
inference(res,[status(thm),theory(equality)],[6,18]),
[iquote('0:Res:6.0,18.1')] ).
cnf(38,plain,
( in(skc6,powerset(skc5))
| empty(powerset(skc5)) ),
inference(res,[status(thm),theory(equality)],[6,16]),
[iquote('0:Res:6.0,16.0')] ).
cnf(39,plain,
~ empty(powerset(skc5)),
inference(mrr,[status(thm)],[37,29]),
[iquote('0:MRR:37.1,29.0')] ).
cnf(40,plain,
in(skc6,powerset(skc5)),
inference(mrr,[status(thm)],[38,39]),
[iquote('0:MRR:38.1,39.0')] ).
cnf(41,plain,
~ subset(skc6,skc5),
inference(res,[status(thm),theory(equality)],[3,35]),
[iquote('0:Res:3.0,35.1')] ).
cnf(117,plain,
( ~ in(u,powerset(v))
| subset(u,v) ),
inference(eqr,[status(thm),theory(equality)],[23]),
[iquote('0:EqR:23.1')] ).
cnf(118,plain,
subset(skc6,skc5),
inference(res,[status(thm),theory(equality)],[40,117]),
[iquote('0:Res:40.0,117.0')] ).
cnf(123,plain,
$false,
inference(mrr,[status(thm)],[118,41]),
[iquote('0:MRR:118.0,41.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU169+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.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 : Sat Jun 18 22:33:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 86 clauses, backtracked 0 clauses, performed 0 splits and kept 70 clauses.
% 0.21/0.45 SPASS allocated 97859 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.45 0:00:00.03 for the input.
% 0.21/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.00 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 2, length 18 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : l3_subset_1 t7_boole d2_subset_1 d3_tarski d1_zfmisc_1
% 0.21/0.45
%------------------------------------------------------------------------------