TSTP Solution File: SET009+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 05:22:23 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 5 unt; 12 nHn; 25 RR)
% Number of literals : 52 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 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('SET009+3.p',unknown),
[] ).
cnf(3,axiom,
~ subset(difference(skc5,skc4),difference(skc5,skc3)),
file('SET009+3.p',unknown),
[] ).
cnf(4,axiom,
( subset(u,v)
| member(skf1(v,u),u) ),
file('SET009+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,difference(v,w))
| member(u,v) ),
file('SET009+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(skf1(u,v),u)
| subset(w,u) ),
file('SET009+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,v)
| ~ member(u,difference(w,v)) ),
file('SET009+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET009+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| member(u,w)
| member(u,difference(v,w)) ),
file('SET009+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(40,plain,
( ~ subset(u,difference(v,w))
| ~ member(skf1(x,u),w)
| subset(u,x) ),
inference(res,[status(thm),theory(equality)],[20,7]),
[iquote('0:Res:20.2,7.1')] ).
cnf(83,plain,
( subset(u,difference(u,v))
| member(skf1(difference(u,v),u),v)
| subset(w,difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[4,31]),
[iquote('0:Res:4.1,31.0')] ).
cnf(85,plain,
( subset(difference(u,v),difference(u,w))
| member(skf1(difference(u,w),difference(u,v)),w)
| subset(x,difference(u,w)) ),
inference(res,[status(thm),theory(equality)],[18,31]),
[iquote('0:Res:18.1,31.0')] ).
cnf(90,plain,
( subset(u,difference(u,v))
| member(skf1(difference(u,v),u),v) ),
inference(con,[status(thm)],[83]),
[iquote('0:Con:83.2')] ).
cnf(95,plain,
( subset(difference(u,v),difference(u,w))
| member(skf1(difference(u,w),difference(u,v)),w) ),
inference(con,[status(thm)],[85]),
[iquote('0:Con:85.2')] ).
cnf(103,plain,
( subset(u,difference(u,skc3))
| member(skf1(difference(u,skc3),u),skc4) ),
inference(res,[status(thm),theory(equality)],[90,10]),
[iquote('0:Res:90.1,10.0')] ).
cnf(115,plain,
( subset(difference(u,skc4),difference(difference(u,skc4),skc3))
| subset(difference(u,skc4),difference(difference(u,skc4),skc3)) ),
inference(res,[status(thm),theory(equality)],[103,19]),
[iquote('0:Res:103.1,19.0')] ).
cnf(117,plain,
subset(difference(u,skc4),difference(difference(u,skc4),skc3)),
inference(obv,[status(thm),theory(equality)],[115]),
[iquote('0:Obv:115.0')] ).
cnf(124,plain,
( ~ member(skf1(u,difference(v,skc4)),skc3)
| subset(difference(v,skc4),u) ),
inference(res,[status(thm),theory(equality)],[117,40]),
[iquote('0:Res:117.0,40.0')] ).
cnf(303,plain,
( subset(difference(u,skc4),difference(u,skc3))
| subset(difference(u,skc4),difference(u,skc3)) ),
inference(res,[status(thm),theory(equality)],[95,124]),
[iquote('0:Res:95.1,124.0')] ).
cnf(305,plain,
subset(difference(u,skc4),difference(u,skc3)),
inference(obv,[status(thm),theory(equality)],[303]),
[iquote('0:Obv:303.0')] ).
cnf(306,plain,
$false,
inference(unc,[status(thm)],[305,3]),
[iquote('0:UnC:305.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 09:52:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 241 clauses, backtracked 0 clauses, performed 0 splits and kept 130 clauses.
% 0.19/0.45 SPASS allocated 85399 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.02 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 6, length 25 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : prove_subset_difference subset_defn difference_defn
% 0.19/0.45
%------------------------------------------------------------------------------