TSTP Solution File: SEU325+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU325+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 14:36:17 EDT 2022

% Result   : Theorem 80.64s 80.81s
% Output   : Refutation 80.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   31
% Syntax   : Number of clauses     :   65 (  46 unt;   1 nHn;  65 RR)
%            Number of literals    :   94 (   0 equ;  36 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   23 (  22 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    one_sorted_str(skc30),
    file('SEU325+2.p',unknown),
    [] ).

cnf(15,axiom,
    relation_empty_yielding(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(19,axiom,
    epsilon_transitive(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(20,axiom,
    epsilon_connected(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(21,axiom,
    ordinal(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(25,axiom,
    v1_membered(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(26,axiom,
    v2_membered(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(27,axiom,
    v3_membered(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(28,axiom,
    v4_membered(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(29,axiom,
    v5_membered(empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(49,axiom,
    relation(skc326),
    file('SEU325+2.p',unknown),
    [] ).

cnf(50,axiom,
    function(skc326),
    file('SEU325+2.p',unknown),
    [] ).

cnf(51,axiom,
    one_to_one(skc326),
    file('SEU325+2.p',unknown),
    [] ).

cnf(52,axiom,
    empty(skc326),
    file('SEU325+2.p',unknown),
    [] ).

cnf(84,axiom,
    ~ empty_carrier(skc30),
    file('SEU325+2.p',unknown),
    [] ).

cnf(85,axiom,
    is_a_cover_of_carrier(skc30,empty_set),
    file('SEU325+2.p',unknown),
    [] ).

cnf(101,axiom,
    empty(skf367(u)),
    file('SEU325+2.p',unknown),
    [] ).

cnf(108,axiom,
    natural(skf367(u)),
    file('SEU325+2.p',unknown),
    [] ).

cnf(109,axiom,
    finite(skf367(u)),
    file('SEU325+2.p',unknown),
    [] ).

cnf(214,axiom,
    equal(set_difference(u,empty_set),u),
    file('SEU325+2.p',unknown),
    [] ).

cnf(220,axiom,
    element(empty_set,powerset(powerset(the_carrier(skc30)))),
    file('SEU325+2.p',unknown),
    [] ).

cnf(285,axiom,
    ( ~ empty(u)
    | equal(u,empty_set) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(304,axiom,
    ( ~ being_limit_ordinal(u)
    | equal(union(u),u) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(431,axiom,
    ( ~ one_sorted_str(u)
    | equal(cast_as_carrier_subset(u),the_carrier(u)) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(488,axiom,
    ( ~ one_sorted_str(u)
    | ~ empty(cast_as_carrier_subset(u))
    | empty_carrier(u) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(523,axiom,
    ( ~ ordinal(u)
    | being_limit_ordinal(u)
    | in(skf575(u),u) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(712,axiom,
    ( ~ element(u,powerset(v))
    | equal(set_difference(v,u),subset_complement(v,u)) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(723,axiom,
    ( ~ in(u,v)
    | ~ element(v,powerset(w))
    | in(u,w) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(729,axiom,
    ( ~ element(u,powerset(powerset(v)))
    | equal(union_of_subsets(v,u),union(u)) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(872,axiom,
    ( ~ in(u,v)
    | ~ element(v,powerset(w))
    | ~ in(u,subset_complement(w,v)) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(1054,axiom,
    ( ~ one_sorted_str(u)
    | ~ is_a_cover_of_carrier(u,v)
    | ~ element(v,powerset(powerset(the_carrier(u))))
    | equal(union_of_subsets(the_carrier(u),v),cast_as_carrier_subset(u)) ),
    file('SEU325+2.p',unknown),
    [] ).

cnf(1324,plain,
    ( ~ one_sorted_str(u)
    | ~ empty(the_carrier(u))
    | empty_carrier(u) ),
    inference(rew,[status(thm),theory(equality)],[431,488]),
    [iquote('0:Rew:431.1,488.1')] ).

cnf(1397,plain,
    ( ~ one_sorted_str(u)
    | ~ is_a_cover_of_carrier(u,v)
    | ~ element(v,powerset(powerset(the_carrier(u))))
    | equal(union(v),the_carrier(u)) ),
    inference(rew,[status(thm),theory(equality)],[729,1054,431]),
    [iquote('0:Rew:729.1,1054.3,431.1,1054.3')] ).

cnf(1472,plain,
    ( ~ empty(the_carrier(skc30))
    | empty_carrier(skc30) ),
    inference(res,[status(thm),theory(equality)],[1,1324]),
    [iquote('0:Res:1.0,1324.0')] ).

cnf(1529,plain,
    ( ~ one_sorted_str(skc30)
    | ~ is_a_cover_of_carrier(skc30,empty_set)
    | equal(union(empty_set),the_carrier(skc30)) ),
    inference(res,[status(thm),theory(equality)],[220,1397]),
    [iquote('0:Res:220.0,1397.2')] ).

cnf(1580,plain,
    ( ~ in(u,subset_complement(powerset(the_carrier(skc30)),empty_set))
    | ~ in(u,empty_set) ),
    inference(res,[status(thm),theory(equality)],[220,872]),
    [iquote('0:Res:220.0,872.0')] ).

cnf(1582,plain,
    equal(set_difference(powerset(the_carrier(skc30)),empty_set),subset_complement(powerset(the_carrier(skc30)),empty_set)),
    inference(res,[status(thm),theory(equality)],[220,712]),
    [iquote('0:Res:220.0,712.0')] ).

cnf(1584,plain,
    ( ~ in(u,empty_set)
    | in(u,powerset(the_carrier(skc30))) ),
    inference(res,[status(thm),theory(equality)],[220,723]),
    [iquote('0:Res:220.0,723.0')] ).

cnf(1604,plain,
    ~ empty(the_carrier(skc30)),
    inference(mrr,[status(thm)],[1472,84]),
    [iquote('0:MRR:1472.1,84.0')] ).

cnf(1608,plain,
    equal(subset_complement(powerset(the_carrier(skc30)),empty_set),powerset(the_carrier(skc30))),
    inference(rew,[status(thm),theory(equality)],[214,1582]),
    [iquote('0:Rew:214.0,1582.0')] ).

cnf(1610,plain,
    equal(union(empty_set),the_carrier(skc30)),
    inference(mrr,[status(thm)],[1529,1,85]),
    [iquote('0:MRR:1529.0,1529.1,1.0,85.0')] ).

cnf(1613,plain,
    ( ~ in(u,powerset(the_carrier(skc30)))
    | ~ in(u,empty_set) ),
    inference(rew,[status(thm),theory(equality)],[1608,1580]),
    [iquote('0:Rew:1608.0,1580.0')] ).

cnf(1614,plain,
    ~ in(u,empty_set),
    inference(mrr,[status(thm)],[1613,1584]),
    [iquote('0:MRR:1613.0,1584.1')] ).

cnf(1775,plain,
    equal(skf367(u),empty_set),
    inference(ems,[status(thm)],[285,101]),
    [iquote('0:EmS:285.0,101.0')] ).

cnf(1778,plain,
    equal(empty_set,skc326),
    inference(ems,[status(thm)],[285,52]),
    [iquote('0:EmS:285.0,52.0')] ).

cnf(1784,plain,
    relation_empty_yielding(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,15]),
    [iquote('0:Rew:1778.0,15.0')] ).

cnf(1785,plain,
    epsilon_transitive(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,19]),
    [iquote('0:Rew:1778.0,19.0')] ).

cnf(1786,plain,
    epsilon_connected(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,20]),
    [iquote('0:Rew:1778.0,20.0')] ).

cnf(1788,plain,
    v1_membered(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,25]),
    [iquote('0:Rew:1778.0,25.0')] ).

cnf(1789,plain,
    v2_membered(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,26]),
    [iquote('0:Rew:1778.0,26.0')] ).

cnf(1790,plain,
    v3_membered(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,27]),
    [iquote('0:Rew:1778.0,27.0')] ).

cnf(1791,plain,
    v4_membered(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,28]),
    [iquote('0:Rew:1778.0,28.0')] ).

cnf(1792,plain,
    v5_membered(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,29]),
    [iquote('0:Rew:1778.0,29.0')] ).

cnf(1794,plain,
    ordinal(skc326),
    inference(rew,[status(thm),theory(equality)],[1778,21]),
    [iquote('0:Rew:1778.0,21.0')] ).

cnf(1802,plain,
    ~ in(u,skc326),
    inference(rew,[status(thm),theory(equality)],[1778,1614]),
    [iquote('0:Rew:1778.0,1614.0')] ).

cnf(1805,plain,
    equal(union(skc326),the_carrier(skc30)),
    inference(rew,[status(thm),theory(equality)],[1778,1610]),
    [iquote('0:Rew:1778.0,1610.0')] ).

cnf(1949,plain,
    equal(skf367(u),skc326),
    inference(rew,[status(thm),theory(equality)],[1778,1775]),
    [iquote('0:Rew:1778.0,1775.0')] ).

cnf(1950,plain,
    natural(skc326),
    inference(rew,[status(thm),theory(equality)],[1949,108]),
    [iquote('0:Rew:1949.0,108.0')] ).

cnf(1954,plain,
    finite(skc326),
    inference(rew,[status(thm),theory(equality)],[1949,109]),
    [iquote('0:Rew:1949.0,109.0')] ).

cnf(2073,plain,
    ( ~ being_limit_ordinal(skc326)
    | equal(the_carrier(skc30),skc326) ),
    inference(spr,[status(thm),theory(equality)],[304,1805]),
    [iquote('0:SpR:304.1,1805.0')] ).

cnf(3575,plain,
    ( ~ ordinal(skc326)
    | being_limit_ordinal(skc326) ),
    inference(res,[status(thm),theory(equality)],[523,1802]),
    [iquote('0:Res:523.2,1802.0')] ).

cnf(3584,plain,
    being_limit_ordinal(skc326),
    inference(ssi,[status(thm)],[3575,51,52,50,49,1784,1785,1786,1788,1789,1790,1791,1792,1794,1950,1954]),
    [iquote('0:SSi:3575.0,51.0,52.0,50.0,49.0,1784.0,1785.0,1786.0,1788.0,1789.0,1790.0,1791.0,1792.0,1794.0,1950.0,1954.0')] ).

cnf(3585,plain,
    equal(the_carrier(skc30),skc326),
    inference(mrr,[status(thm)],[2073,3584]),
    [iquote('0:MRR:2073.0,3584.0')] ).

cnf(3586,plain,
    ~ empty(skc326),
    inference(rew,[status(thm),theory(equality)],[3585,1604]),
    [iquote('0:Rew:3585.0,1604.0')] ).

cnf(3683,plain,
    $false,
    inference(mrr,[status(thm)],[3586,52]),
    [iquote('0:MRR:3586.0,52.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU325+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n010.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 Jun 19 18:22:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 80.64/80.81  
% 80.64/80.81  SPASS V 3.9 
% 80.64/80.81  SPASS beiseite: Proof found.
% 80.64/80.81  % SZS status Theorem
% 80.64/80.81  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 80.64/80.81  SPASS derived 2088 clauses, backtracked 38 clauses, performed 12 splits and kept 2412 clauses.
% 80.64/80.81  SPASS allocated 165622 KBytes.
% 80.64/80.81  SPASS spent	0:1:20.41 on the problem.
% 80.64/80.81  		0:00:00.04 for the input.
% 80.64/80.81  		0:1:18.87 for the FLOTTER CNF translation.
% 80.64/80.81  		0:00:00.03 for inferences.
% 80.64/80.81  		0:00:00.01 for the backtracking.
% 80.64/80.81  		0:00:01.13 for the reduction.
% 80.64/80.81  
% 80.64/80.81  
% 80.64/80.81  Here is a proof with depth 2, length 65 :
% 80.64/80.81  % SZS output start Refutation
% See solution above
% 80.64/80.81  Formulae used in the proof : t5_tops_2 fc2_ordinal1 fc6_membered rc1_partfun1 rc2_finset_1 t3_boole t6_boole d6_ordinal1 t12_pre_topc fc2_pre_topc t41_ordinal1 rc3_ordinal1 d5_subset_1 l3_subset_1 redefinition_k5_setfam_1 t54_subset_1 d8_pre_topc
% 80.64/80.81  
%------------------------------------------------------------------------------