TSTP Solution File: NUM409+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 : Mon Jul 18 14:25:56 EDT 2022

% Result   : Theorem 0.21s 0.47s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   37 (  21 unt;   0 nHn;  37 RR)
%            Number of literals    :   67 (   0 equ;  33 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    relation_empty_yielding(empty_set),
    file('NUM409+1.p',unknown),
    [] ).

cnf(7,axiom,
    function(empty_set),
    file('NUM409+1.p',unknown),
    [] ).

cnf(8,axiom,
    one_to_one(empty_set),
    file('NUM409+1.p',unknown),
    [] ).

cnf(10,axiom,
    epsilon_transitive(empty_set),
    file('NUM409+1.p',unknown),
    [] ).

cnf(11,axiom,
    epsilon_connected(empty_set),
    file('NUM409+1.p',unknown),
    [] ).

cnf(12,axiom,
    ordinal(empty_set),
    file('NUM409+1.p',unknown),
    [] ).

cnf(20,axiom,
    empty(skc22),
    file('NUM409+1.p',unknown),
    [] ).

cnf(21,axiom,
    relation(skc22),
    file('NUM409+1.p',unknown),
    [] ).

cnf(55,axiom,
    subset(empty_set,u),
    file('NUM409+1.p',unknown),
    [] ).

cnf(56,axiom,
    ~ transfinite_sequence_of(empty_set,skc15),
    file('NUM409+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ empty(u)
    | function(u) ),
    file('NUM409+1.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ empty(u)
    | relation(u) ),
    file('NUM409+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ empty(u)
    | empty(relation_dom(u)) ),
    file('NUM409+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ empty(u)
    | empty(relation_rng(u)) ),
    file('NUM409+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ empty(u)
    | equal(u,empty_set) ),
    file('NUM409+1.p',unknown),
    [] ).

cnf(89,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ ordinal(relation_dom(u))
    | transfinite_sequence(u) ),
    file('NUM409+1.p',unknown),
    [] ).

cnf(98,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ transfinite_sequence(u)
    | ~ subset(relation_rng(u),v)
    | transfinite_sequence_of(u,v) ),
    file('NUM409+1.p',unknown),
    [] ).

cnf(107,plain,
    equal(empty_set,skc22),
    inference(ems,[status(thm)],[74,20]),
    [iquote('0:EmS:74.0,20.0')] ).

cnf(111,plain,
    relation_empty_yielding(skc22),
    inference(rew,[status(thm),theory(equality)],[107,6]),
    [iquote('0:Rew:107.0,6.0')] ).

cnf(112,plain,
    one_to_one(skc22),
    inference(rew,[status(thm),theory(equality)],[107,8]),
    [iquote('0:Rew:107.0,8.0')] ).

cnf(113,plain,
    epsilon_connected(skc22),
    inference(rew,[status(thm),theory(equality)],[107,11]),
    [iquote('0:Rew:107.0,11.0')] ).

cnf(114,plain,
    epsilon_transitive(skc22),
    inference(rew,[status(thm),theory(equality)],[107,10]),
    [iquote('0:Rew:107.0,10.0')] ).

cnf(115,plain,
    ordinal(skc22),
    inference(rew,[status(thm),theory(equality)],[107,12]),
    [iquote('0:Rew:107.0,12.0')] ).

cnf(116,plain,
    function(skc22),
    inference(rew,[status(thm),theory(equality)],[107,7]),
    [iquote('0:Rew:107.0,7.0')] ).

cnf(119,plain,
    subset(skc22,u),
    inference(rew,[status(thm),theory(equality)],[107,55]),
    [iquote('0:Rew:107.0,55.0')] ).

cnf(120,plain,
    ~ transfinite_sequence_of(skc22,skc15),
    inference(rew,[status(thm),theory(equality)],[107,56]),
    [iquote('0:Rew:107.0,56.0')] ).

cnf(121,plain,
    ( ~ empty(u)
    | equal(u,skc22) ),
    inference(rew,[status(thm),theory(equality)],[107,74]),
    [iquote('0:Rew:107.0,74.1')] ).

cnf(145,plain,
    ( ~ empty(u)
    | equal(relation_dom(u),skc22) ),
    inference(ems,[status(thm)],[121,70]),
    [iquote('0:EmS:121.0,70.1')] ).

cnf(146,plain,
    ( ~ empty(u)
    | equal(relation_rng(u),skc22) ),
    inference(ems,[status(thm)],[121,72]),
    [iquote('0:EmS:121.0,72.1')] ).

cnf(206,plain,
    ( ~ empty(u)
    | ~ function(u)
    | ~ relation(u)
    | ~ ordinal(skc22)
    | transfinite_sequence(u) ),
    inference(spl,[status(thm),theory(equality)],[145,89]),
    [iquote('0:SpL:145.1,89.2')] ).

cnf(210,plain,
    ( ~ empty(u)
    | ~ ordinal(skc22)
    | transfinite_sequence(u) ),
    inference(ssi,[status(thm)],[206,62,59]),
    [iquote('0:SSi:206.2,206.1,62.1,59.1')] ).

cnf(211,plain,
    ( ~ empty(u)
    | transfinite_sequence(u) ),
    inference(mrr,[status(thm)],[210,115]),
    [iquote('0:MRR:210.1,115.0')] ).

cnf(259,plain,
    ( ~ empty(u)
    | ~ relation(u)
    | ~ function(u)
    | ~ transfinite_sequence(u)
    | ~ subset(skc22,v)
    | transfinite_sequence_of(u,v) ),
    inference(spl,[status(thm),theory(equality)],[146,98]),
    [iquote('0:SpL:146.1,98.3')] ).

cnf(262,plain,
    ( ~ empty(u)
    | ~ subset(skc22,v)
    | transfinite_sequence_of(u,v) ),
    inference(ssi,[status(thm)],[259,211,59,62]),
    [iquote('0:SSi:259.3,259.2,259.1,211.1,59.1,62.1')] ).

cnf(263,plain,
    ( ~ empty(u)
    | transfinite_sequence_of(u,v) ),
    inference(mrr,[status(thm)],[262,119]),
    [iquote('0:MRR:262.1,119.0')] ).

cnf(266,plain,
    ~ empty(skc22),
    inference(res,[status(thm),theory(equality)],[263,120]),
    [iquote('0:Res:263.1,120.0')] ).

cnf(270,plain,
    $false,
    inference(ssi,[status(thm)],[266,21,20,111,112,113,114,115,116]),
    [iquote('0:SSi:266.0,21.0,20.0,111.0,112.0,113.0,114.0,115.0,116.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jul  7 23:14:14 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.47  
% 0.21/0.47  SPASS V 3.9 
% 0.21/0.47  SPASS beiseite: Proof found.
% 0.21/0.47  % SZS status Theorem
% 0.21/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.47  SPASS derived 139 clauses, backtracked 0 clauses, performed 0 splits and kept 157 clauses.
% 0.21/0.47  SPASS allocated 97836 KBytes.
% 0.21/0.47  SPASS spent	0:00:00.11 on the problem.
% 0.21/0.47  		0:00:00.03 for the input.
% 0.21/0.47  		0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.47  		0:00:00.00 for inferences.
% 0.21/0.47  		0:00:00.00 for the backtracking.
% 0.21/0.47  		0:00:00.01 for the reduction.
% 0.21/0.47  
% 0.21/0.47  
% 0.21/0.47  Here is a proof with depth 3, length 37 :
% 0.21/0.47  % SZS output start Refutation
% See solution above
% 0.21/0.47  Formulae used in the proof : fc2_ordinal1 rc1_relat_1 t2_xboole_1 t45_ordinal1 cc1_funct_1 cc1_relat_1 fc7_relat_1 fc8_relat_1 t6_boole d7_ordinal1 d8_ordinal1
% 0.21/0.47  
%------------------------------------------------------------------------------