TSTP Solution File: SET347+4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 05:25:48 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 7 unt; 1 nHn; 11 RR)
% Number of literals : 16 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ member(u,empty_set),
file('SET347+4.p',unknown),
[] ).
cnf(2,axiom,
~ equal_set(sum__dfg(empty_set),empty_set),
file('SET347+4.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET347+4.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,sum__dfg(v))
| member(skf4(u,v),v) ),
file('SET347+4.p',unknown),
[] ).
cnf(24,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal_set(v,u) ),
file('SET347+4.p',unknown),
[] ).
cnf(31,plain,
( ~ subset(empty_set,sum__dfg(empty_set))
| ~ subset(sum__dfg(empty_set),empty_set) ),
inference(res,[status(thm),theory(equality)],[24,2]),
[iquote('0:Res:24.2,2.0')] ).
cnf(34,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.1,1.0')] ).
cnf(37,plain,
~ subset(sum__dfg(empty_set),empty_set),
inference(mrr,[status(thm)],[31,34]),
[iquote('0:MRR:31.0,34.0')] ).
cnf(58,plain,
~ member(u,sum__dfg(empty_set)),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.1,1.0')] ).
cnf(64,plain,
subset(sum__dfg(empty_set),u),
inference(res,[status(thm),theory(equality)],[7,58]),
[iquote('0:Res:7.1,58.0')] ).
cnf(67,plain,
$false,
inference(unc,[status(thm)],[64,37]),
[iquote('0:UnC:64.0,37.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.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 03:08:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 35 clauses, backtracked 0 clauses, performed 0 splits and kept 62 clauses.
% 0.20/0.45 SPASS allocated 85399 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.45 0:00:00.03 for the input.
% 0.20/0.45 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.00 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 2, length 11 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : empty_set thI38 subset sum__dfg product equal_set
% 0.20/0.45
%------------------------------------------------------------------------------