TSTP Solution File: SET200+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET200+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:24:59 EDT 2022
% Result : Theorem 17.54s 17.79s
% Output : Refutation 17.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 12 unt; 18 nHn; 42 RR)
% Number of literals : 88 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc7,skc6),
file('SET200+3.p',unknown),
[] ).
cnf(2,axiom,
subset(skc4,skc5),
file('SET200+3.p',unknown),
[] ).
cnf(4,axiom,
equal(union(u,v),union(v,u)),
file('SET200+3.p',unknown),
[] ).
cnf(5,axiom,
~ subset(union(skc7,skc4),union(skc6,skc5)),
file('SET200+3.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET200+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,v)
| member(u,union(v,w)) ),
file('SET200+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(u,v)
| member(u,union(w,v)) ),
file('SET200+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET200+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET200+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET200+3.p',unknown),
[] ).
cnf(14,axiom,
( equal(u,v)
| member(skf3(v,u),v)
| member(skf3(v,u),u) ),
file('SET200+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(skf3(u,v),u)
| ~ member(skf3(u,v),v)
| equal(v,u) ),
file('SET200+3.p',unknown),
[] ).
cnf(16,plain,
~ subset(union(skc4,skc7),union(skc5,skc6)),
inference(rew,[status(thm),theory(equality)],[4,5]),
[iquote('0:Rew:4.0,5.0,4.0,5.0')] ).
cnf(17,plain,
( ~ member(u,skc4)
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.0')] ).
cnf(18,plain,
( ~ member(u,skc7)
| member(u,skc6) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(31,plain,
( ~ member(skf2(union(u,v),w),v)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.0')] ).
cnf(32,plain,
( ~ member(skf2(union(u,v),w),u)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,9]),
[iquote('0:Res:7.1,9.0')] ).
cnf(57,plain,
( subset(union(u,v),w)
| member(skf2(w,union(u,v)),u)
| member(skf2(w,union(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[6,13]),
[iquote('0:Res:6.1,13.0')] ).
cnf(74,plain,
( ~ subset(u,v)
| equal(w,u)
| member(skf3(u,w),w)
| member(skf3(u,w),v) ),
inference(res,[status(thm),theory(equality)],[14,10]),
[iquote('0:Res:14.1,10.0')] ).
cnf(79,plain,
( equal(union(u,v),w)
| member(skf3(w,union(u,v)),w)
| member(skf3(w,union(u,v)),u)
| member(skf3(w,union(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[14,13]),
[iquote('0:Res:14.2,13.0')] ).
cnf(138,plain,
( ~ member(skf2(union(u,skc5),v),skc4)
| subset(w,union(u,skc5)) ),
inference(res,[status(thm),theory(equality)],[17,31]),
[iquote('0:Res:17.1,31.0')] ).
cnf(150,plain,
( ~ member(skf2(union(union(u,v),w),x),v)
| subset(y,union(union(u,v),w)) ),
inference(res,[status(thm),theory(equality)],[8,32]),
[iquote('0:Res:8.1,32.0')] ).
cnf(152,plain,
( subset(u,union(u,v))
| subset(w,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[6,32]),
[iquote('0:Res:6.1,32.0')] ).
cnf(155,plain,
subset(u,union(u,v)),
inference(con,[status(thm)],[152]),
[iquote('0:Con:152.1')] ).
cnf(211,plain,
( equal(u,v)
| member(skf3(v,u),u)
| member(skf3(v,u),union(v,w)) ),
inference(res,[status(thm),theory(equality)],[155,74]),
[iquote('0:Res:155.0,74.0')] ).
cnf(319,plain,
( subset(union(u,skc4),union(v,skc5))
| member(skf2(union(v,skc5),union(u,skc4)),u)
| subset(w,union(v,skc5)) ),
inference(res,[status(thm),theory(equality)],[57,138]),
[iquote('0:Res:57.2,138.0')] ).
cnf(326,plain,
( subset(union(u,skc4),union(v,skc5))
| member(skf2(union(v,skc5),union(u,skc4)),u) ),
inference(con,[status(thm)],[319]),
[iquote('0:Con:319.2')] ).
cnf(525,plain,
( equal(union(u,v),u)
| member(skf3(u,union(u,v)),u)
| member(skf3(u,union(u,v)),v) ),
inference(fac,[status(thm)],[79]),
[iquote('0:Fac:79.1,79.2')] ).
cnf(2467,plain,
( ~ member(skf3(u,union(u,v)),union(u,v))
| equal(union(u,v),u)
| member(skf3(u,union(u,v)),v)
| equal(union(u,v),u) ),
inference(res,[status(thm),theory(equality)],[525,15]),
[iquote('0:Res:525.1,15.0')] ).
cnf(2471,plain,
( ~ member(skf3(u,union(u,v)),union(u,v))
| member(skf3(u,union(u,v)),v)
| equal(union(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[2467]),
[iquote('0:Obv:2467.1')] ).
cnf(16673,plain,
( equal(union(u,v),u)
| member(skf3(u,union(u,v)),union(u,v)) ),
inference(fac,[status(thm)],[211]),
[iquote('0:Fac:211.1,211.2')] ).
cnf(16681,plain,
( member(skf3(u,union(u,v)),v)
| equal(union(u,v),u) ),
inference(mrr,[status(thm)],[2471,16673]),
[iquote('0:MRR:2471.0,16673.1')] ).
cnf(16753,plain,
( equal(union(u,skc7),u)
| member(skf3(u,union(u,skc7)),skc6) ),
inference(res,[status(thm),theory(equality)],[16681,18]),
[iquote('0:Res:16681.0,18.0')] ).
cnf(19977,plain,
( subset(union(u,skc4),union(union(v,u),skc5))
| subset(w,union(union(v,u),skc5)) ),
inference(res,[status(thm),theory(equality)],[326,150]),
[iquote('0:Res:326.1,150.0')] ).
cnf(19998,plain,
subset(union(u,skc4),union(union(v,u),skc5)),
inference(con,[status(thm)],[19977]),
[iquote('0:Con:19977.1')] ).
cnf(19999,plain,
subset(union(u,skc4),union(skc5,union(v,u))),
inference(rew,[status(thm),theory(equality)],[4,19998]),
[iquote('0:Rew:4.0,19998.0')] ).
cnf(20014,plain,
subset(union(skc4,u),union(skc5,union(v,u))),
inference(spr,[status(thm),theory(equality)],[4,19999]),
[iquote('0:SpR:4.0,19999.0')] ).
cnf(20548,plain,
( ~ member(skf3(skc6,union(skc6,skc7)),union(skc6,skc7))
| equal(union(skc6,skc7),skc6)
| equal(union(skc6,skc7),skc6) ),
inference(res,[status(thm),theory(equality)],[16753,15]),
[iquote('0:Res:16753.1,15.0')] ).
cnf(20553,plain,
( ~ member(skf3(skc6,union(skc6,skc7)),union(skc6,skc7))
| equal(union(skc6,skc7),skc6) ),
inference(obv,[status(thm),theory(equality)],[20548]),
[iquote('0:Obv:20548.1')] ).
cnf(20554,plain,
equal(union(skc6,skc7),skc6),
inference(mrr,[status(thm)],[20553,16673]),
[iquote('0:MRR:20553.0,16673.1')] ).
cnf(20850,plain,
subset(union(skc4,skc7),union(skc5,skc6)),
inference(spr,[status(thm),theory(equality)],[20554,20014]),
[iquote('0:SpR:20554.0,20014.0')] ).
cnf(21044,plain,
$false,
inference(mrr,[status(thm)],[20850,16]),
[iquote('0:MRR:20850.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET200+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 : Sun Jul 10 23:01:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 17.54/17.79
% 17.54/17.79 SPASS V 3.9
% 17.54/17.79 SPASS beiseite: Proof found.
% 17.54/17.79 % SZS status Theorem
% 17.54/17.79 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.54/17.79 SPASS derived 16398 clauses, backtracked 2175 clauses, performed 6 splits and kept 7766 clauses.
% 17.54/17.79 SPASS allocated 98989 KBytes.
% 17.54/17.79 SPASS spent 0:0:17.38 on the problem.
% 17.54/17.79 0:00:00.03 for the input.
% 17.54/17.79 0:00:00.03 for the FLOTTER CNF translation.
% 17.54/17.79 0:00:00.21 for inferences.
% 17.54/17.79 0:00:00.16 for the backtracking.
% 17.54/17.79 0:0:16.88 for the reduction.
% 17.54/17.79
% 17.54/17.79
% 17.54/17.79 Here is a proof with depth 6, length 42 :
% 17.54/17.79 % SZS output start Refutation
% See solution above
% 17.54/17.80 Formulae used in the proof : prove_th34 commutativity_of_union subset_defn union_defn equal_member_defn
% 17.54/17.80
%------------------------------------------------------------------------------