TSTP Solution File: SEU296+3 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU296+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 14:35:58 EDT 2022

% Result   : Theorem 0.60s 0.80s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   19
% Syntax   : Number of clauses     :   42 (  12 unt;   0 nHn;  42 RR)
%            Number of literals    :  104 (   0 equ;  66 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    finite(skc24),
    file('SEU296+3.p',unknown),
    [] ).

cnf(2,axiom,
    function(skc23),
    file('SEU296+3.p',unknown),
    [] ).

cnf(3,axiom,
    relation(skc23),
    file('SEU296+3.p',unknown),
    [] ).

cnf(81,axiom,
    relation(skf6(u)),
    file('SEU296+3.p',unknown),
    [] ).

cnf(102,axiom,
    subset(u,u),
    file('SEU296+3.p',unknown),
    [] ).

cnf(105,axiom,
    ~ finite(relation_image(skc23,skc24)),
    file('SEU296+3.p',unknown),
    [] ).

cnf(120,axiom,
    subset(set_intersection2(u,v),u),
    file('SEU296+3.p',unknown),
    [] ).

cnf(126,axiom,
    ( ~ finite(u)
    | function(skf6(u)) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(135,axiom,
    ( ~ finite(u)
    | finite(set_intersection2(v,u)) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(145,axiom,
    ( ~ finite(u)
    | equal(relation_rng(skf6(u)),u) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(146,axiom,
    ( ~ finite(u)
    | in(relation_dom(skf6(u)),omega) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(148,axiom,
    ( ~ subset(u,v)
    | element(u,powerset(v)) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(159,axiom,
    ( ~ finite(u)
    | ~ element(v,powerset(u))
    | finite(v) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(160,axiom,
    ( ~ relation(u)
    | ~ relation(v)
    | relation(relation_composition(v,u)) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(173,axiom,
    ( ~ relation(u)
    | equal(relation_image(u,set_intersection2(relation_dom(u),v)),relation_image(u,v)) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(174,axiom,
    ( ~ relation(u)
    | ~ relation(v)
    | equal(relation_image(u,relation_rng(v)),relation_rng(relation_composition(v,u))) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(176,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ function(v)
    | ~ relation(v)
    | function(relation_composition(v,u)) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(177,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_rng(u),v)
    | ~ in(relation_dom(u),omega)
    | finite(v) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(181,axiom,
    ( ~ relation(u)
    | ~ relation(v)
    | ~ subset(relation_rng(v),relation_dom(u))
    | equal(relation_dom(relation_composition(v,u)),relation_dom(v)) ),
    file('SEU296+3.p',unknown),
    [] ).

cnf(189,plain,
    equal(relation_image(skc23,set_intersection2(relation_dom(skc23),u)),relation_image(skc23,u)),
    inference(res,[status(thm),theory(equality)],[3,173]),
    [iquote('0:Res:3.0,173.0')] ).

cnf(199,plain,
    ( ~ relation(u)
    | ~ subset(relation_rng(u),relation_dom(skc23))
    | equal(relation_dom(relation_composition(u,skc23)),relation_dom(u)) ),
    inference(res,[status(thm),theory(equality)],[3,181]),
    [iquote('0:Res:3.0,181.1')] ).

cnf(200,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ function(skc23)
    | function(relation_composition(u,skc23)) ),
    inference(res,[status(thm),theory(equality)],[3,176]),
    [iquote('0:Res:3.0,176.3')] ).

cnf(201,plain,
    ( ~ relation(u)
    | equal(relation_image(skc23,relation_rng(u)),relation_rng(relation_composition(u,skc23))) ),
    inference(res,[status(thm),theory(equality)],[3,174]),
    [iquote('0:Res:3.0,174.1')] ).

cnf(202,plain,
    ( ~ relation(u)
    | relation(relation_composition(u,skc23)) ),
    inference(res,[status(thm),theory(equality)],[3,160]),
    [iquote('0:Res:3.0,160.1')] ).

cnf(220,plain,
    finite(set_intersection2(u,skc24)),
    inference(res,[status(thm),theory(equality)],[1,135]),
    [iquote('0:Res:1.0,135.0')] ).

cnf(225,plain,
    ( ~ finite(u)
    | ~ element(relation_image(skc23,skc24),powerset(u)) ),
    inference(res,[status(thm),theory(equality)],[159,105]),
    [iquote('0:Res:159.2,105.0')] ).

cnf(231,plain,
    ( ~ function(u)
    | ~ relation(u)
    | function(relation_composition(u,skc23)) ),
    inference(mrr,[status(thm)],[200,2]),
    [iquote('0:MRR:200.2,2.0')] ).

cnf(848,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ in(relation_dom(u),omega)
    | finite(relation_rng(u)) ),
    inference(eqr,[status(thm),theory(equality)],[177]),
    [iquote('0:EqR:177.2')] ).

cnf(1036,plain,
    ( ~ finite(u)
    | ~ subset(relation_image(skc23,skc24),u) ),
    inference(res,[status(thm),theory(equality)],[148,225]),
    [iquote('0:Res:148.1,225.1')] ).

cnf(1066,plain,
    ~ finite(relation_image(skc23,skc24)),
    inference(res,[status(thm),theory(equality)],[102,1036]),
    [iquote('0:Res:102.0,1036.1')] ).

cnf(1351,plain,
    ( ~ finite(u)
    | ~ relation(skf6(u))
    | equal(relation_rng(relation_composition(skf6(u),skc23)),relation_image(skc23,u)) ),
    inference(spr,[status(thm),theory(equality)],[145,201]),
    [iquote('0:SpR:145.1,201.1')] ).

cnf(1358,plain,
    ( ~ finite(u)
    | equal(relation_rng(relation_composition(skf6(u),skc23)),relation_image(skc23,u)) ),
    inference(ssi,[status(thm)],[1351,81,126]),
    [iquote('0:SSi:1351.1,81.1,126.0')] ).

cnf(1830,plain,
    ( ~ finite(u)
    | ~ relation(skf6(u))
    | ~ subset(u,relation_dom(skc23))
    | equal(relation_dom(relation_composition(skf6(u),skc23)),relation_dom(skf6(u))) ),
    inference(spl,[status(thm),theory(equality)],[145,199]),
    [iquote('0:SpL:145.1,199.1')] ).

cnf(1839,plain,
    ( ~ finite(u)
    | ~ subset(u,relation_dom(skc23))
    | equal(relation_dom(relation_composition(skf6(u),skc23)),relation_dom(skf6(u))) ),
    inference(ssi,[status(thm)],[1830,81,126]),
    [iquote('0:SSi:1830.1,81.1,126.0')] ).

cnf(2699,plain,
    ( ~ finite(u)
    | ~ function(relation_composition(skf6(u),skc23))
    | ~ relation(relation_composition(skf6(u),skc23))
    | ~ subset(u,relation_dom(skc23))
    | ~ in(relation_dom(skf6(u)),omega)
    | finite(relation_rng(relation_composition(skf6(u),skc23))) ),
    inference(spl,[status(thm),theory(equality)],[1839,848]),
    [iquote('0:SpL:1839.2,848.2')] ).

cnf(2709,plain,
    ( ~ finite(u)
    | ~ function(relation_composition(skf6(u),skc23))
    | ~ relation(relation_composition(skf6(u),skc23))
    | ~ subset(u,relation_dom(skc23))
    | ~ in(relation_dom(skf6(u)),omega)
    | finite(relation_image(skc23,u)) ),
    inference(rew,[status(thm),theory(equality)],[1358,2699]),
    [iquote('0:Rew:1358.1,2699.5')] ).

cnf(2710,plain,
    ( ~ finite(u)
    | ~ subset(u,relation_dom(skc23))
    | ~ in(relation_dom(skf6(u)),omega)
    | finite(relation_image(skc23,u)) ),
    inference(ssi,[status(thm)],[2709,202,81,126,231]),
    [iquote('0:SSi:2709.2,2709.1,202.1,81.0,126.2,231.1,81.0,126.1,202.1,81.0,126.2,231.1,81.0,126.1')] ).

cnf(2711,plain,
    ( ~ finite(u)
    | ~ subset(u,relation_dom(skc23))
    | finite(relation_image(skc23,u)) ),
    inference(mrr,[status(thm)],[2710,146]),
    [iquote('0:MRR:2710.2,146.1')] ).

cnf(3901,plain,
    ( ~ finite(set_intersection2(relation_dom(skc23),u))
    | finite(relation_image(skc23,set_intersection2(relation_dom(skc23),u))) ),
    inference(res,[status(thm),theory(equality)],[120,2711]),
    [iquote('0:Res:120.0,2711.1')] ).

cnf(3923,plain,
    ( ~ finite(set_intersection2(relation_dom(skc23),u))
    | finite(relation_image(skc23,u)) ),
    inference(rew,[status(thm),theory(equality)],[189,3901]),
    [iquote('0:Rew:189.0,3901.1')] ).

cnf(3949,plain,
    finite(relation_image(skc23,skc24)),
    inference(sor,[status(thm)],[3923,220]),
    [iquote('0:SoR:3923.0,220.0')] ).

cnf(3951,plain,
    $false,
    inference(mrr,[status(thm)],[3949,1066]),
    [iquote('0:MRR:3949.0,1066.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13  % Problem  : SEU296+3 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n028.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jun 19 20:36:45 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.60/0.80  
% 0.60/0.80  SPASS V 3.9 
% 0.60/0.80  SPASS beiseite: Proof found.
% 0.60/0.80  % SZS status Theorem
% 0.60/0.80  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.60/0.80  SPASS derived 2948 clauses, backtracked 10 clauses, performed 3 splits and kept 1317 clauses.
% 0.60/0.80  SPASS allocated 100761 KBytes.
% 0.60/0.80  SPASS spent	0:00:00.42 on the problem.
% 0.60/0.80  		0:00:00.03 for the input.
% 0.60/0.80  		0:00:00.04 for the FLOTTER CNF translation.
% 0.60/0.80  		0:00:00.04 for inferences.
% 0.60/0.80  		0:00:00.00 for the backtracking.
% 0.60/0.80  		0:00:00.26 for the reduction.
% 0.60/0.80  
% 0.60/0.80  
% 0.60/0.80  Here is a proof with depth 5, length 42 :
% 0.60/0.80  % SZS output start Refutation
% See solution above
% 0.60/0.80  Formulae used in the proof : t17_finset_1 d1_finset_1 rc5_funct_1 reflexivity_r1_tarski t17_xboole_1 fc10_finset_1 t3_subset cc2_finset_1 dt_k5_relat_1 t145_relat_1 t160_relat_1 fc1_funct_1 t46_relat_1
% 0.60/0.80  
%------------------------------------------------------------------------------