TSTP Solution File: SEU221+3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU221+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 14:35:11 EDT 2022

% Result   : Theorem 1.10s 1.27s
% Output   : Refutation 1.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   41 (   9 unt;  17 nHn;  41 RR)
%            Number of literals    :  149 (   0 equ;  92 neg)
%            Maximal clause size   :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    relation(skc9),
    file('SEU221+3.p',unknown),
    [] ).

cnf(2,axiom,
    function(skc9),
    file('SEU221+3.p',unknown),
    [] ).

cnf(3,axiom,
    one_to_one(skc9),
    file('SEU221+3.p',unknown),
    [] ).

cnf(28,axiom,
    ~ one_to_one(function_inverse(skc9)),
    file('SEU221+3.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | relation(function_inverse(u)) ),
    file('SEU221+3.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | function(function_inverse(u)) ),
    file('SEU221+3.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | one_to_one(u)
    | in(skf10(u),relation_dom(u)) ),
    file('SEU221+3.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | one_to_one(u)
    | in(skf9(u),relation_dom(u)) ),
    file('SEU221+3.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(skf10(u),skf9(u))
    | one_to_one(u) ),
    file('SEU221+3.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | one_to_one(u)
    | equal(apply(u,skf10(u)),apply(u,skf9(u))) ),
    file('SEU221+3.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ one_to_one(u)
    | ~ in(v,relation_rng(u))
    | equal(apply(u,apply(function_inverse(u),v)),v) ),
    file('SEU221+3.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ one_to_one(v)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(u,function_inverse(v))
    | equal(relation_dom(u),relation_rng(v)) ),
    file('SEU221+3.p',unknown),
    [] ).

cnf(90,plain,
    ( ~ function(skc9)
    | ~ relation(skc9)
    | ~ in(u,relation_rng(skc9))
    | equal(apply(skc9,apply(function_inverse(skc9),u)),u) ),
    inference(res,[status(thm),theory(equality)],[3,71]),
    [iquote('0:Res:3.0,71.0')] ).

cnf(107,plain,
    ( ~ relation(skc9)
    | relation(function_inverse(skc9)) ),
    inference(res,[status(thm),theory(equality)],[2,46]),
    [iquote('0:Res:2.0,46.1')] ).

cnf(108,plain,
    ( ~ relation(skc9)
    | function(function_inverse(skc9)) ),
    inference(res,[status(thm),theory(equality)],[2,47]),
    [iquote('0:Res:2.0,47.1')] ).

cnf(123,plain,
    ( ~ function(skc9)
    | ~ one_to_one(skc9)
    | ~ relation(u)
    | ~ function(u)
    | ~ equal(u,function_inverse(skc9))
    | equal(relation_dom(u),relation_rng(skc9)) ),
    inference(res,[status(thm),theory(equality)],[1,74]),
    [iquote('0:Res:1.0,74.0')] ).

cnf(155,plain,
    relation(function_inverse(skc9)),
    inference(mrr,[status(thm)],[107,1]),
    [iquote('0:MRR:107.0,1.0')] ).

cnf(156,plain,
    function(function_inverse(skc9)),
    inference(mrr,[status(thm)],[108,1]),
    [iquote('0:MRR:108.0,1.0')] ).

cnf(159,plain,
    ( ~ in(u,relation_rng(skc9))
    | equal(apply(skc9,apply(function_inverse(skc9),u)),u) ),
    inference(mrr,[status(thm)],[90,2,1]),
    [iquote('0:MRR:90.0,90.1,2.0,1.0')] ).

cnf(164,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(u,function_inverse(skc9))
    | equal(relation_dom(u),relation_rng(skc9)) ),
    inference(mrr,[status(thm)],[123,2,3]),
    [iquote('0:MRR:123.0,123.1,2.0,3.0')] ).

cnf(554,plain,
    ( ~ function(function_inverse(u))
    | ~ relation(function_inverse(u))
    | ~ relation(u)
    | ~ function(u)
    | ~ one_to_one(u)
    | ~ in(skf10(function_inverse(u)),relation_rng(u))
    | one_to_one(function_inverse(u))
    | equal(apply(u,apply(function_inverse(u),skf9(function_inverse(u)))),skf10(function_inverse(u))) ),
    inference(spr,[status(thm),theory(equality)],[68,71]),
    [iquote('0:SpR:68.3,71.4')] ).

cnf(555,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ one_to_one(u)
    | ~ in(skf10(function_inverse(u)),relation_rng(u))
    | one_to_one(function_inverse(u))
    | equal(apply(u,apply(function_inverse(u),skf9(function_inverse(u)))),skf10(function_inverse(u))) ),
    inference(ssi,[status(thm)],[554,47,46]),
    [iquote('0:SSi:554.1,554.0,47.2,46.2,47.2,46.2')] ).

cnf(939,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ function(u)
    | ~ relation(u)
    | ~ equal(u,function_inverse(skc9))
    | one_to_one(u)
    | in(skf9(u),relation_rng(skc9)) ),
    inference(spr,[status(thm),theory(equality)],[164,63]),
    [iquote('0:SpR:164.3,63.3')] ).

cnf(940,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ function(u)
    | ~ relation(u)
    | ~ equal(u,function_inverse(skc9))
    | one_to_one(u)
    | in(skf10(u),relation_rng(skc9)) ),
    inference(spr,[status(thm),theory(equality)],[164,62]),
    [iquote('0:SpR:164.3,62.3')] ).

cnf(953,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(u,function_inverse(skc9))
    | one_to_one(u)
    | in(skf10(u),relation_rng(skc9)) ),
    inference(obv,[status(thm),theory(equality)],[940]),
    [iquote('0:Obv:940.1')] ).

cnf(954,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(u,function_inverse(skc9))
    | one_to_one(u)
    | in(skf9(u),relation_rng(skc9)) ),
    inference(obv,[status(thm),theory(equality)],[939]),
    [iquote('0:Obv:939.1')] ).

cnf(1339,plain,
    ( ~ relation(skc9)
    | ~ function(skc9)
    | ~ one_to_one(skc9)
    | ~ in(skf10(function_inverse(skc9)),relation_rng(skc9))
    | ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
    | one_to_one(function_inverse(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(spr,[status(thm),theory(equality)],[555,159]),
    [iquote('0:SpR:555.5,159.1')] ).

cnf(1350,plain,
    ( ~ in(skf10(function_inverse(skc9)),relation_rng(skc9))
    | ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
    | one_to_one(function_inverse(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(ssi,[status(thm)],[1339,3,2,1]),
    [iquote('0:SSi:1339.2,1339.1,1339.0,3.0,2.0,1.0,3.0,2.0,1.0,3.0,2.0,1.0')] ).

cnf(1351,plain,
    ( ~ in(skf10(function_inverse(skc9)),relation_rng(skc9))
    | ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(mrr,[status(thm)],[1350,28]),
    [iquote('0:MRR:1350.2,28.0')] ).

cnf(2742,plain,
    ( ~ function(function_inverse(skc9))
    | ~ relation(function_inverse(skc9))
    | ~ equal(function_inverse(skc9),function_inverse(skc9))
    | ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
    | one_to_one(function_inverse(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(res,[status(thm),theory(equality)],[953,1351]),
    [iquote('0:Res:953.4,1351.0')] ).

cnf(2744,plain,
    ( ~ function(function_inverse(skc9))
    | ~ relation(function_inverse(skc9))
    | ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
    | one_to_one(function_inverse(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(obv,[status(thm),theory(equality)],[2742]),
    [iquote('0:Obv:2742.2')] ).

cnf(2745,plain,
    ( ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
    | one_to_one(function_inverse(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(ssi,[status(thm)],[2744,155,156]),
    [iquote('0:SSi:2744.1,2744.0,155.0,156.0,155.0,156.0')] ).

cnf(2746,plain,
    ( ~ in(skf9(function_inverse(skc9)),relation_rng(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(mrr,[status(thm)],[2745,28]),
    [iquote('0:MRR:2745.1,28.0')] ).

cnf(2753,plain,
    ( ~ function(function_inverse(skc9))
    | ~ relation(function_inverse(skc9))
    | ~ equal(function_inverse(skc9),function_inverse(skc9))
    | one_to_one(function_inverse(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(res,[status(thm),theory(equality)],[954,2746]),
    [iquote('0:Res:954.4,2746.0')] ).

cnf(2755,plain,
    ( ~ function(function_inverse(skc9))
    | ~ relation(function_inverse(skc9))
    | one_to_one(function_inverse(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(obv,[status(thm),theory(equality)],[2753]),
    [iquote('0:Obv:2753.2')] ).

cnf(2756,plain,
    ( one_to_one(function_inverse(skc9))
    | equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))) ),
    inference(ssi,[status(thm)],[2755,155,156]),
    [iquote('0:SSi:2755.1,2755.0,155.0,156.0,155.0,156.0')] ).

cnf(2757,plain,
    equal(skf10(function_inverse(skc9)),skf9(function_inverse(skc9))),
    inference(mrr,[status(thm)],[2756,28]),
    [iquote('0:MRR:2756.0,28.0')] ).

cnf(2779,plain,
    ( ~ function(function_inverse(skc9))
    | ~ relation(function_inverse(skc9))
    | ~ equal(skf9(function_inverse(skc9)),skf9(function_inverse(skc9)))
    | one_to_one(function_inverse(skc9)) ),
    inference(spl,[status(thm),theory(equality)],[2757,64]),
    [iquote('0:SpL:2757.0,64.2')] ).

cnf(2782,plain,
    ( ~ function(function_inverse(skc9))
    | ~ relation(function_inverse(skc9))
    | one_to_one(function_inverse(skc9)) ),
    inference(obv,[status(thm),theory(equality)],[2779]),
    [iquote('0:Obv:2779.2')] ).

cnf(2783,plain,
    one_to_one(function_inverse(skc9)),
    inference(ssi,[status(thm)],[2782,155,156]),
    [iquote('0:SSi:2782.1,2782.0,155.0,156.0,155.0,156.0')] ).

cnf(2784,plain,
    $false,
    inference(mrr,[status(thm)],[2783,28]),
    [iquote('0:MRR:2783.0,28.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU221+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n006.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 : Mon Jun 20 11:35:10 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.10/1.27  
% 1.10/1.27  SPASS V 3.9 
% 1.10/1.27  SPASS beiseite: Proof found.
% 1.10/1.27  % SZS status Theorem
% 1.10/1.27  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.10/1.27  SPASS derived 2217 clauses, backtracked 19 clauses, performed 2 splits and kept 1320 clauses.
% 1.10/1.27  SPASS allocated 100713 KBytes.
% 1.10/1.27  SPASS spent	0:00:00.92 on the problem.
% 1.10/1.27  		0:00:00.03 for the input.
% 1.10/1.27  		0:00:00.08 for the FLOTTER CNF translation.
% 1.10/1.27  		0:00:00.05 for inferences.
% 1.10/1.27  		0:00:00.00 for the backtracking.
% 1.10/1.27  		0:00:00.71 for the reduction.
% 1.10/1.27  
% 1.10/1.27  
% 1.10/1.27  Here is a proof with depth 5, length 41 :
% 1.10/1.27  % SZS output start Refutation
% See solution above
% 1.10/1.27  Formulae used in the proof : t62_funct_1 dt_k2_funct_1 d8_funct_1 t57_funct_1 t54_funct_1
% 1.10/1.27  
%------------------------------------------------------------------------------