TSTP Solution File: SET588+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 05:27:10 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 22 ( 5 unt; 10 nHn; 22 RR)
% Number of literals : 47 ( 0 equ; 17 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc3,skc4),
file('SET588+3.p',unknown),
[] ).
cnf(3,axiom,
~ subset(difference(skc3,skc5),difference(skc4,skc5)),
file('SET588+3.p',unknown),
[] ).
cnf(4,axiom,
( subset(u,v)
| member(skf1(v,u),u) ),
file('SET588+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,difference(v,w))
| member(u,v) ),
file('SET588+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(skf1(u,v),u)
| subset(w,u) ),
file('SET588+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,v)
| ~ member(u,difference(w,v)) ),
file('SET588+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET588+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| member(u,w)
| member(u,difference(v,w)) ),
file('SET588+3.p',unknown),
[] ).
cnf(10,plain,
( ~ member(u,skc3)
| member(u,skc4) ),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.0,8.0')] ).
cnf(18,plain,
( subset(difference(u,v),w)
| member(skf1(w,difference(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[4,5]),
[iquote('0:Res:4.1,5.0')] ).
cnf(19,plain,
( ~ member(skf1(u,difference(v,w)),w)
| subset(difference(v,w),u) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.1,7.1')] ).
cnf(20,plain,
( ~ subset(u,v)
| subset(u,w)
| member(skf1(w,u),v) ),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.1,8.0')] ).
cnf(31,plain,
( ~ member(skf1(difference(u,v),w),u)
| member(skf1(difference(u,v),w),v)
| subset(x,difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[9,6]),
[iquote('0:Res:9.2,6.0')] ).
cnf(32,plain,
( subset(difference(skc3,u),v)
| member(skf1(v,difference(skc3,u)),skc4) ),
inference(res,[status(thm),theory(equality)],[18,10]),
[iquote('0:Res:18.1,10.0')] ).
cnf(44,plain,
( subset(difference(skc3,u),skc4)
| subset(v,skc4) ),
inference(res,[status(thm),theory(equality)],[32,6]),
[iquote('0:Res:32.1,6.0')] ).
cnf(45,plain,
subset(difference(skc3,u),skc4),
inference(con,[status(thm)],[44]),
[iquote('0:Con:44.1')] ).
cnf(87,plain,
( ~ subset(u,v)
| subset(u,difference(v,w))
| member(skf1(difference(v,w),u),w)
| subset(x,difference(v,w)) ),
inference(res,[status(thm),theory(equality)],[20,31]),
[iquote('0:Res:20.2,31.0')] ).
cnf(94,plain,
( ~ subset(u,v)
| subset(u,difference(v,w))
| member(skf1(difference(v,w),u),w) ),
inference(con,[status(thm)],[87]),
[iquote('0:Con:87.3')] ).
cnf(255,plain,
( ~ subset(difference(u,v),w)
| subset(difference(u,v),difference(w,v))
| subset(difference(u,v),difference(w,v)) ),
inference(res,[status(thm),theory(equality)],[94,19]),
[iquote('0:Res:94.2,19.0')] ).
cnf(258,plain,
( ~ subset(difference(u,v),w)
| subset(difference(u,v),difference(w,v)) ),
inference(obv,[status(thm),theory(equality)],[255]),
[iquote('0:Obv:255.1')] ).
cnf(522,plain,
~ subset(difference(skc3,skc5),skc4),
inference(res,[status(thm),theory(equality)],[258,3]),
[iquote('0:Res:258.1,3.0')] ).
cnf(525,plain,
$false,
inference(mrr,[status(thm)],[522,45]),
[iquote('0:MRR:522.0,45.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 21:20:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.51
% 0.20/0.51 SPASS V 3.9
% 0.20/0.51 SPASS beiseite: Proof found.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.51 SPASS derived 418 clauses, backtracked 0 clauses, performed 0 splits and kept 221 clauses.
% 0.20/0.51 SPASS allocated 85700 KBytes.
% 0.20/0.51 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.51 0:00:00.03 for the input.
% 0.20/0.51 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.51 0:00:00.01 for inferences.
% 0.20/0.51 0:00:00.00 for the backtracking.
% 0.20/0.51 0:00:00.05 for the reduction.
% 0.20/0.51
% 0.20/0.51
% 0.20/0.51 Here is a proof with depth 4, length 22 :
% 0.20/0.51 % SZS output start Refutation
% See solution above
% 0.20/0.51 Formulae used in the proof : prove_difference_subset1 subset_defn difference_defn
% 0.20/0.51
%------------------------------------------------------------------------------