TSTP Solution File: SET366+4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 05:25:56 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 1 nHn; 7 RR)
% Number of literals : 9 ( 0 equ; 4 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; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ member(u,empty_set),
file('SET366+4.p',unknown),
[] ).
cnf(2,axiom,
~ member(empty_set,power_set(skc1)),
file('SET366+4.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET366+4.p',unknown),
[] ).
cnf(9,axiom,
( ~ subset(u,v)
| member(u,power_set(v)) ),
file('SET366+4.p',unknown),
[] ).
cnf(31,plain,
~ subset(empty_set,skc1),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.1,2.0')] ).
cnf(43,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.1,1.0')] ).
cnf(46,plain,
$false,
inference(unc,[status(thm)],[43,31]),
[iquote('0:UnC:43.0,31.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 : Mon Jul 11 02:12:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 36 clauses.
% 0.19/0.44 SPASS allocated 85336 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.03 for the input.
% 0.19/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.00 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 1, length 7 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : empty_set thI47 subset power_set
% 0.19/0.44
%------------------------------------------------------------------------------