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  
%------------------------------------------------------------------------------