TSTP Solution File: SEU030+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU030+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 14:33:38 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   31 (  14 unt;   0 nHn;  31 RR)
%            Number of literals    :   89 (   0 equ;  67 neg)
%            Maximal clause size   :   10 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    relation(skc11),
    file('SEU030+1.p',unknown),
    [] ).

cnf(2,axiom,
    relation(skc10),
    file('SEU030+1.p',unknown),
    [] ).

cnf(3,axiom,
    function(skc10),
    file('SEU030+1.p',unknown),
    [] ).

cnf(4,axiom,
    function(skc11),
    file('SEU030+1.p',unknown),
    [] ).

cnf(5,axiom,
    one_to_one(skc10),
    file('SEU030+1.p',unknown),
    [] ).

cnf(35,axiom,
    equal(relation_rng(skc10),relation_dom(skc11)),
    file('SEU030+1.p',unknown),
    [] ).

cnf(36,axiom,
    ~ equal(function_inverse(skc10),skc11),
    file('SEU030+1.p',unknown),
    [] ).

cnf(47,axiom,
    equal(relation_composition(skc10,skc11),identity_relation(relation_dom(skc10))),
    file('SEU030+1.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | relation(function_inverse(u)) ),
    file('SEU030+1.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | function(function_inverse(u)) ),
    file('SEU030+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ one_to_one(u)
    | ~ function(u)
    | ~ relation(u)
    | equal(relation_rng(function_inverse(u)),relation_dom(u)) ),
    file('SEU030+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ one_to_one(u)
    | ~ function(u)
    | ~ relation(u)
    | equal(relation_composition(function_inverse(u),u),identity_relation(relation_rng(u))) ),
    file('SEU030+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ relation(v)
    | ~ function(v)
    | ~ relation(w)
    | ~ function(w)
    | ~ equal(relation_rng(u),x)
    | ~ equal(relation_composition(v,w),identity_relation(x))
    | ~ equal(relation_composition(u,v),identity_relation(relation_dom(w)))
    | equal(w,u) ),
    file('SEU030+1.p',unknown),
    [] ).

cnf(76,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | equal(relation_composition(function_inverse(skc10),skc10),identity_relation(relation_rng(skc10))) ),
    inference(res,[status(thm),theory(equality)],[5,72]),
    [iquote('0:Res:5.0,72.2')] ).

cnf(78,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | equal(relation_rng(function_inverse(skc10)),relation_dom(skc10)) ),
    inference(res,[status(thm),theory(equality)],[5,68]),
    [iquote('0:Res:5.0,68.2')] ).

cnf(96,plain,
    ( ~ relation(skc10)
    | relation(function_inverse(skc10)) ),
    inference(res,[status(thm),theory(equality)],[3,53]),
    [iquote('0:Res:3.0,53.1')] ).

cnf(97,plain,
    ( ~ relation(skc10)
    | function(function_inverse(skc10)) ),
    inference(res,[status(thm),theory(equality)],[3,54]),
    [iquote('0:Res:3.0,54.1')] ).

cnf(142,plain,
    ( ~ function(skc11)
    | ~ relation(skc11)
    | ~ function(u)
    | ~ relation(u)
    | ~ function(function_inverse(skc10))
    | ~ relation(function_inverse(skc10))
    | ~ equal(relation_rng(function_inverse(skc10)),v)
    | ~ equal(relation_composition(u,skc11),identity_relation(v))
    | ~ equal(relation_composition(function_inverse(skc10),u),identity_relation(relation_dom(skc11))) ),
    inference(res,[status(thm),theory(equality)],[73,36]),
    [iquote('0:Res:73.9,36.0')] ).

cnf(146,plain,
    relation(function_inverse(skc10)),
    inference(mrr,[status(thm)],[96,2]),
    [iquote('0:MRR:96.0,2.0')] ).

cnf(147,plain,
    function(function_inverse(skc10)),
    inference(mrr,[status(thm)],[97,2]),
    [iquote('0:MRR:97.0,2.0')] ).

cnf(151,plain,
    equal(relation_rng(function_inverse(skc10)),relation_dom(skc10)),
    inference(mrr,[status(thm)],[78,2,3]),
    [iquote('0:MRR:78.0,78.1,2.0,3.0')] ).

cnf(161,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | equal(relation_composition(function_inverse(skc10),skc10),identity_relation(relation_dom(skc11))) ),
    inference(rew,[status(thm),theory(equality)],[35,76]),
    [iquote('0:Rew:35.0,76.2')] ).

cnf(162,plain,
    equal(relation_composition(function_inverse(skc10),skc10),identity_relation(relation_dom(skc11))),
    inference(mrr,[status(thm)],[161,2,3]),
    [iquote('0:MRR:161.0,161.1,2.0,3.0')] ).

cnf(176,plain,
    ( ~ function(skc11)
    | ~ relation(skc11)
    | ~ function(u)
    | ~ relation(u)
    | ~ function(function_inverse(skc10))
    | ~ relation(function_inverse(skc10))
    | ~ equal(relation_dom(skc10),v)
    | ~ equal(relation_composition(u,skc11),identity_relation(v))
    | ~ equal(relation_composition(function_inverse(skc10),u),identity_relation(relation_dom(skc11))) ),
    inference(rew,[status(thm),theory(equality)],[151,142]),
    [iquote('0:Rew:151.0,142.6')] ).

cnf(177,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ equal(relation_dom(skc10),v)
    | ~ equal(relation_composition(u,skc11),identity_relation(v))
    | ~ equal(relation_composition(function_inverse(skc10),u),identity_relation(relation_dom(skc11))) ),
    inference(mrr,[status(thm)],[176,4,1,147,146]),
    [iquote('0:MRR:176.0,176.1,176.4,176.5,4.0,1.0,147.0,146.0')] ).

cnf(919,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ equal(relation_dom(skc10),u)
    | ~ equal(relation_composition(skc10,skc11),identity_relation(u))
    | ~ equal(identity_relation(relation_dom(skc11)),identity_relation(relation_dom(skc11))) ),
    inference(spl,[status(thm),theory(equality)],[162,177]),
    [iquote('0:SpL:162.0,177.4')] ).

cnf(922,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ equal(relation_dom(skc10),u)
    | ~ equal(relation_composition(skc10,skc11),identity_relation(u)) ),
    inference(obv,[status(thm),theory(equality)],[919]),
    [iquote('0:Obv:919.4')] ).

cnf(923,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ equal(relation_dom(skc10),u)
    | ~ equal(identity_relation(relation_dom(skc10)),identity_relation(u)) ),
    inference(rew,[status(thm),theory(equality)],[47,922]),
    [iquote('0:Rew:47.0,922.3')] ).

cnf(924,plain,
    ( ~ equal(relation_dom(skc10),u)
    | ~ equal(identity_relation(relation_dom(skc10)),identity_relation(u)) ),
    inference(ssi,[status(thm)],[923,5,3,2]),
    [iquote('0:SSi:923.1,923.0,5.0,3.0,2.0,5.0,3.0,2.0')] ).

cnf(1004,plain,
    ~ equal(relation_dom(skc10),relation_dom(skc10)),
    inference(eqr,[status(thm),theory(equality)],[924]),
    [iquote('0:EqR:924.1')] ).

cnf(1006,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[1004]),
    [iquote('0:Obv:1004.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU030+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jun 18 23:32:02 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.51  
% 0.19/0.51  SPASS V 3.9 
% 0.19/0.51  SPASS beiseite: Proof found.
% 0.19/0.51  % SZS status Theorem
% 0.19/0.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.51  SPASS derived 689 clauses, backtracked 0 clauses, performed 0 splits and kept 325 clauses.
% 0.19/0.51  SPASS allocated 98437 KBytes.
% 0.19/0.51  SPASS spent	0:00:00.16 on the problem.
% 0.19/0.51  		0:00:00.03 for the input.
% 0.19/0.51  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.51  		0:00:00.01 for inferences.
% 0.19/0.51  		0:00:00.00 for the backtracking.
% 0.19/0.51  		0:00:00.05 for the reduction.
% 0.19/0.51  
% 0.19/0.51  
% 0.19/0.51  Here is a proof with depth 3, length 31 :
% 0.19/0.51  % SZS output start Refutation
% See solution above
% 0.19/0.51  Formulae used in the proof : t63_funct_1 dt_k2_funct_1 t55_funct_1 t61_funct_1 l72_funct_1
% 0.19/0.51  
%------------------------------------------------------------------------------