TSTP Solution File: SEU270+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU270+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:35:43 EDT 2022
% Result : Theorem 107.68s 107.85s
% Output : Refutation 107.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of clauses : 58 ( 17 unt; 9 nHn; 58 RR)
% Number of literals : 160 ( 0 equ; 94 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ordinal(skc10),
file('SEU270+1.p',unknown),
[] ).
cnf(36,axiom,
relation(inclusion_relation(u)),
file('SEU270+1.p',unknown),
[] ).
cnf(40,axiom,
~ connected(inclusion_relation(skc10)),
file('SEU270+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ ordinal(u)
| epsilon_transitive(u) ),
file('SEU270+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ ordinal(u)
| epsilon_connected(u) ),
file('SEU270+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ ordinal(u)
| ~ in(v,u)
| ordinal(v) ),
file('SEU270+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ relation(u)
| ~ is_connected_in(u,relation_field(u))
| connected(u) ),
file('SEU270+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ relation(u)
| is_connected_in(u,v)
| in(skf8(v,w),v) ),
file('SEU270+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ relation(u)
| is_connected_in(u,v)
| in(skf7(v,w),v) ),
file('SEU270+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ordinal(u)
| ~ ordinal(v)
| ordinal_subset(u,v)
| ordinal_subset(v,u) ),
file('SEU270+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ relation(u)
| ~ equal(u,inclusion_relation(v))
| equal(relation_field(u),v) ),
file('SEU270+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ordinal(u)
| ~ ordinal(v)
| ~ ordinal_subset(v,u)
| subset(v,u) ),
file('SEU270+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ relation(u)
| ~ in(ordered_pair(skf8(v,u),skf7(v,u)),u)
| is_connected_in(u,v) ),
file('SEU270+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ relation(u)
| ~ in(ordered_pair(skf7(v,u),skf8(v,u)),u)
| is_connected_in(u,v) ),
file('SEU270+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ relation(u)
| ~ subset(v,w)
| ~ in(w,x)
| ~ in(v,x)
| ~ equal(u,inclusion_relation(x))
| in(ordered_pair(v,w),u) ),
file('SEU270+1.p',unknown),
[] ).
cnf(94,plain,
( ~ in(u,skc10)
| ordinal(u) ),
inference(res,[status(thm),theory(equality)],[1,63]),
[iquote('0:Res:1.0,63.0')] ).
cnf(96,plain,
epsilon_transitive(skc10),
inference(res,[status(thm),theory(equality)],[1,43]),
[iquote('0:Res:1.0,43.0')] ).
cnf(97,plain,
epsilon_connected(skc10),
inference(res,[status(thm),theory(equality)],[1,44]),
[iquote('0:Res:1.0,44.0')] ).
cnf(209,plain,
( ~ relation(u)
| is_connected_in(u,skc10)
| ordinal(skf7(skc10,v)) ),
inference(res,[status(thm),theory(equality)],[72,94]),
[iquote('0:Res:72.2,94.0')] ).
cnf(216,plain,
( ~ relation(u)
| is_connected_in(u,skc10) ),
inference(spt,[spt(split,[position(s1)])],[209]),
[iquote('1:Spt:209.0,209.1')] ).
cnf(217,plain,
( ~ relation(u)
| is_connected_in(u,skc10)
| ordinal(skf8(skc10,v)) ),
inference(res,[status(thm),theory(equality)],[71,94]),
[iquote('0:Res:71.2,94.0')] ).
cnf(228,plain,
( ~ relation(inclusion_relation(u))
| equal(relation_field(inclusion_relation(u)),u) ),
inference(eqr,[status(thm),theory(equality)],[74]),
[iquote('0:EqR:74.1')] ).
cnf(229,plain,
equal(relation_field(inclusion_relation(u)),u),
inference(ssi,[status(thm)],[228,36]),
[iquote('0:SSi:228.0,36.0')] ).
cnf(232,plain,
( ~ relation(inclusion_relation(u))
| ~ is_connected_in(inclusion_relation(u),u)
| connected(inclusion_relation(u)) ),
inference(spl,[status(thm),theory(equality)],[229,67]),
[iquote('0:SpL:229.0,67.1')] ).
cnf(236,plain,
( ~ is_connected_in(inclusion_relation(u),u)
| connected(inclusion_relation(u)) ),
inference(ssi,[status(thm)],[232,36]),
[iquote('0:SSi:232.0,36.0')] ).
cnf(254,plain,
( ~ relation(inclusion_relation(skc10))
| connected(inclusion_relation(skc10)) ),
inference(res,[status(thm),theory(equality)],[216,236]),
[iquote('1:Res:216.1,236.0')] ).
cnf(255,plain,
connected(inclusion_relation(skc10)),
inference(ssi,[status(thm)],[254,36,1,97,96]),
[iquote('1:SSi:254.0,36.0,1.0,97.0,96.0')] ).
cnf(256,plain,
$false,
inference(mrr,[status(thm)],[255,40]),
[iquote('1:MRR:255.0,40.0')] ).
cnf(258,plain,
ordinal(skf7(skc10,u)),
inference(spt,[spt(split,[position(s2)])],[209]),
[iquote('1:Spt:256.0,209.2')] ).
cnf(315,plain,
( ~ relation(u)
| is_connected_in(u,skc10) ),
inference(spt,[spt(split,[position(s2s1)])],[217]),
[iquote('2:Spt:217.0,217.1')] ).
cnf(316,plain,
( ~ relation(inclusion_relation(skc10))
| connected(inclusion_relation(skc10)) ),
inference(res,[status(thm),theory(equality)],[315,236]),
[iquote('2:Res:315.1,236.0')] ).
cnf(317,plain,
connected(inclusion_relation(skc10)),
inference(ssi,[status(thm)],[316,36,1,97,96]),
[iquote('2:SSi:316.0,36.0,1.0,97.0,96.0')] ).
cnf(318,plain,
$false,
inference(mrr,[status(thm)],[317,40]),
[iquote('2:MRR:317.0,40.0')] ).
cnf(319,plain,
ordinal(skf8(skc10,u)),
inference(spt,[spt(split,[position(s2s2)])],[217]),
[iquote('2:Spt:318.0,217.2')] ).
cnf(464,plain,
( ~ relation(inclusion_relation(u))
| ~ subset(v,w)
| ~ in(w,u)
| ~ in(v,u)
| in(ordered_pair(v,w),inclusion_relation(u)) ),
inference(eqr,[status(thm),theory(equality)],[85]),
[iquote('0:EqR:85.4')] ).
cnf(467,plain,
( ~ subset(u,v)
| ~ in(v,w)
| ~ in(u,w)
| in(ordered_pair(u,v),inclusion_relation(w)) ),
inference(ssi,[status(thm)],[464,36]),
[iquote('0:SSi:464.0,36.0')] ).
cnf(902,plain,
( ~ relation(inclusion_relation(u))
| ~ subset(skf7(v,inclusion_relation(u)),skf8(v,inclusion_relation(u)))
| ~ in(skf8(v,inclusion_relation(u)),u)
| ~ in(skf7(v,inclusion_relation(u)),u)
| is_connected_in(inclusion_relation(u),v) ),
inference(res,[status(thm),theory(equality)],[467,82]),
[iquote('0:Res:467.3,82.1')] ).
cnf(903,plain,
( ~ relation(inclusion_relation(u))
| ~ subset(skf8(v,inclusion_relation(u)),skf7(v,inclusion_relation(u)))
| ~ in(skf7(v,inclusion_relation(u)),u)
| ~ in(skf8(v,inclusion_relation(u)),u)
| is_connected_in(inclusion_relation(u),v) ),
inference(res,[status(thm),theory(equality)],[467,81]),
[iquote('0:Res:467.3,81.1')] ).
cnf(906,plain,
( ~ subset(skf8(u,inclusion_relation(v)),skf7(u,inclusion_relation(v)))
| ~ in(skf7(u,inclusion_relation(v)),v)
| ~ in(skf8(u,inclusion_relation(v)),v)
| is_connected_in(inclusion_relation(v),u) ),
inference(ssi,[status(thm)],[903,36]),
[iquote('0:SSi:903.0,36.0')] ).
cnf(907,plain,
( ~ subset(skf7(u,inclusion_relation(v)),skf8(u,inclusion_relation(v)))
| ~ in(skf8(u,inclusion_relation(v)),v)
| ~ in(skf7(u,inclusion_relation(v)),v)
| is_connected_in(inclusion_relation(v),u) ),
inference(ssi,[status(thm)],[902,36]),
[iquote('0:SSi:902.0,36.0')] ).
cnf(2238,plain,
( ~ ordinal(skf7(u,inclusion_relation(v)))
| ~ ordinal(skf8(u,inclusion_relation(v)))
| ~ ordinal_subset(skf8(u,inclusion_relation(v)),skf7(u,inclusion_relation(v)))
| ~ in(skf7(u,inclusion_relation(v)),v)
| ~ in(skf8(u,inclusion_relation(v)),v)
| is_connected_in(inclusion_relation(v),u) ),
inference(res,[status(thm),theory(equality)],[77,906]),
[iquote('0:Res:77.3,906.0')] ).
cnf(2334,plain,
( ~ ordinal(skf8(u,inclusion_relation(v)))
| ~ ordinal(skf7(u,inclusion_relation(v)))
| ~ ordinal_subset(skf7(u,inclusion_relation(v)),skf8(u,inclusion_relation(v)))
| ~ in(skf8(u,inclusion_relation(v)),v)
| ~ in(skf7(u,inclusion_relation(v)),v)
| is_connected_in(inclusion_relation(v),u) ),
inference(res,[status(thm),theory(equality)],[77,907]),
[iquote('0:Res:77.3,907.0')] ).
cnf(16941,plain,
( ~ ordinal(skf8(skc10,inclusion_relation(u)))
| ~ ordinal_subset(skf8(skc10,inclusion_relation(u)),skf7(skc10,inclusion_relation(u)))
| ~ in(skf7(skc10,inclusion_relation(u)),u)
| ~ in(skf8(skc10,inclusion_relation(u)),u)
| is_connected_in(inclusion_relation(u),skc10) ),
inference(sor,[status(thm)],[2238,258]),
[iquote('1:SoR:2238.0,258.0')] ).
cnf(16944,plain,
( ~ ordinal_subset(skf8(skc10,inclusion_relation(u)),skf7(skc10,inclusion_relation(u)))
| ~ in(skf7(skc10,inclusion_relation(u)),u)
| ~ in(skf8(skc10,inclusion_relation(u)),u)
| is_connected_in(inclusion_relation(u),skc10) ),
inference(ssi,[status(thm)],[16941,319,36]),
[iquote('2:SSi:16941.0,319.0,36.0')] ).
cnf(16977,plain,
( ~ ordinal(skf7(skc10,inclusion_relation(u)))
| ~ ordinal_subset(skf7(skc10,inclusion_relation(u)),skf8(skc10,inclusion_relation(u)))
| ~ in(skf8(skc10,inclusion_relation(u)),u)
| ~ in(skf7(skc10,inclusion_relation(u)),u)
| is_connected_in(inclusion_relation(u),skc10) ),
inference(sor,[status(thm)],[2334,319]),
[iquote('2:SoR:2334.0,319.0')] ).
cnf(16980,plain,
( ~ ordinal_subset(skf7(skc10,inclusion_relation(u)),skf8(skc10,inclusion_relation(u)))
| ~ in(skf8(skc10,inclusion_relation(u)),u)
| ~ in(skf7(skc10,inclusion_relation(u)),u)
| is_connected_in(inclusion_relation(u),skc10) ),
inference(ssi,[status(thm)],[16977,258,36]),
[iquote('2:SSi:16977.0,258.0,36.0')] ).
cnf(34891,plain,
( ~ ordinal(skf7(skc10,inclusion_relation(u)))
| ~ ordinal(skf8(skc10,inclusion_relation(u)))
| ~ in(skf7(skc10,inclusion_relation(u)),u)
| ~ in(skf8(skc10,inclusion_relation(u)),u)
| ordinal_subset(skf7(skc10,inclusion_relation(u)),skf8(skc10,inclusion_relation(u)))
| is_connected_in(inclusion_relation(u),skc10) ),
inference(res,[status(thm),theory(equality)],[73,16944]),
[iquote('2:Res:73.3,16944.0')] ).
cnf(34909,plain,
( ~ in(skf7(skc10,inclusion_relation(u)),u)
| ~ in(skf8(skc10,inclusion_relation(u)),u)
| ordinal_subset(skf7(skc10,inclusion_relation(u)),skf8(skc10,inclusion_relation(u)))
| is_connected_in(inclusion_relation(u),skc10) ),
inference(ssi,[status(thm)],[34891,319,36,258]),
[iquote('2:SSi:34891.1,34891.0,319.0,36.0,258.0,36.0')] ).
cnf(34910,plain,
( ~ in(skf7(skc10,inclusion_relation(u)),u)
| ~ in(skf8(skc10,inclusion_relation(u)),u)
| is_connected_in(inclusion_relation(u),skc10) ),
inference(mrr,[status(thm)],[34909,16980]),
[iquote('2:MRR:34909.2,16980.0')] ).
cnf(34919,plain,
( ~ relation(u)
| ~ in(skf7(skc10,inclusion_relation(skc10)),skc10)
| is_connected_in(u,skc10)
| is_connected_in(inclusion_relation(skc10),skc10) ),
inference(res,[status(thm),theory(equality)],[71,34910]),
[iquote('2:Res:71.2,34910.1')] ).
cnf(34946,plain,
( ~ relation(u)
| is_connected_in(u,skc10)
| is_connected_in(inclusion_relation(skc10),skc10) ),
inference(mrr,[status(thm)],[34919,72]),
[iquote('2:MRR:34919.1,72.2')] ).
cnf(35567,plain,
( ~ relation(u)
| is_connected_in(u,skc10) ),
inference(spt,[spt(split,[position(s2s2s1)])],[34946]),
[iquote('3:Spt:34946.0,34946.1')] ).
cnf(35569,plain,
( ~ relation(inclusion_relation(skc10))
| connected(inclusion_relation(skc10)) ),
inference(res,[status(thm),theory(equality)],[35567,236]),
[iquote('3:Res:35567.1,236.0')] ).
cnf(35570,plain,
connected(inclusion_relation(skc10)),
inference(ssi,[status(thm)],[35569,36,1,97,96]),
[iquote('3:SSi:35569.0,36.0,1.0,97.0,96.0')] ).
cnf(35571,plain,
$false,
inference(mrr,[status(thm)],[35570,40]),
[iquote('3:MRR:35570.0,40.0')] ).
cnf(35573,plain,
is_connected_in(inclusion_relation(skc10),skc10),
inference(spt,[spt(split,[position(s2s2s2)])],[34946]),
[iquote('3:Spt:35571.0,34946.2')] ).
cnf(35580,plain,
connected(inclusion_relation(skc10)),
inference(res,[status(thm),theory(equality)],[35573,236]),
[iquote('3:Res:35573.0,236.0')] ).
cnf(35581,plain,
$false,
inference(mrr,[status(thm)],[35580,40]),
[iquote('3:MRR:35580.0,40.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU270+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 06:27:18 EDT 2022
% 0.13/0.33 % CPUTime :
% 107.68/107.85
% 107.68/107.85 SPASS V 3.9
% 107.68/107.85 SPASS beiseite: Proof found.
% 107.68/107.85 % SZS status Theorem
% 107.68/107.85 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 107.68/107.85 SPASS derived 25940 clauses, backtracked 514 clauses, performed 25 splits and kept 12266 clauses.
% 107.68/107.85 SPASS allocated 153681 KBytes.
% 107.68/107.85 SPASS spent 0:1:44.37 on the problem.
% 107.68/107.85 0:00:00.04 for the input.
% 107.68/107.85 0:00:00.05 for the FLOTTER CNF translation.
% 107.68/107.85 0:00:00.94 for inferences.
% 107.68/107.85 0:00:01.82 for the backtracking.
% 107.68/107.85 0:1:41.10 for the reduction.
% 107.68/107.85
% 107.68/107.85
% 107.68/107.85 Here is a proof with depth 8, length 58 :
% 107.68/107.85 % SZS output start Refutation
% See solution above
% 107.68/107.85 Formulae used in the proof : t4_wellord2 dt_k1_wellord2 cc1_ordinal1 t23_ordinal1 d14_relat_2 d6_relat_2 connectedness_r1_ordinal1 d1_wellord2 reflexivity_r1_tarski redefinition_r1_ordinal1
% 107.68/107.85
%------------------------------------------------------------------------------