TSTP Solution File: SEU023+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 14:33:36 EDT 2022

% Result   : Theorem 0.47s 0.64s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   22 (   9 unt;   0 nHn;  22 RR)
%            Number of literals    :   73 (   0 equ;  59 neg)
%            Maximal clause size   :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    one_to_one(skc10),
    file('SEU023+1.p',unknown),
    [] ).

cnf(2,axiom,
    function(skc10),
    file('SEU023+1.p',unknown),
    [] ).

cnf(3,axiom,
    relation(skc10),
    file('SEU023+1.p',unknown),
    [] ).

cnf(28,axiom,
    in(skc11,relation_dom(skc10)),
    file('SEU023+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | relation(function_inverse(u)) ),
    file('SEU023+1.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | function(function_inverse(u)) ),
    file('SEU023+1.p',unknown),
    [] ).

cnf(65,axiom,
    ( ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11)
    | ~ equal(apply(relation_composition(skc10,function_inverse(skc10)),skc11),skc11) ),
    file('SEU023+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ relation(v)
    | ~ function(v)
    | ~ in(w,relation_dom(u))
    | equal(apply(relation_composition(u,v),w),apply(v,apply(u,w))) ),
    file('SEU023+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ one_to_one(v)
    | ~ function(v)
    | ~ relation(v)
    | ~ in(w,relation_dom(v))
    | ~ equal(u,function_inverse(v))
    | ~ equal(x,apply(v,w))
    | equal(w,apply(u,x)) ),
    file('SEU023+1.p',unknown),
    [] ).

cnf(87,plain,
    ( ~ function(skc10)
    | relation(function_inverse(skc10)) ),
    inference(res,[status(thm),theory(equality)],[3,46]),
    [iquote('0:Res:3.0,46.0')] ).

cnf(88,plain,
    ( ~ function(skc10)
    | function(function_inverse(skc10)) ),
    inference(res,[status(thm),theory(equality)],[3,47]),
    [iquote('0:Res:3.0,47.0')] ).

cnf(142,plain,
    relation(function_inverse(skc10)),
    inference(mrr,[status(thm)],[87,2]),
    [iquote('0:MRR:87.0,2.0')] ).

cnf(143,plain,
    function(function_inverse(skc10)),
    inference(mrr,[status(thm)],[88,2]),
    [iquote('0:MRR:88.0,2.0')] ).

cnf(485,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ relation(function_inverse(skc10))
    | ~ function(function_inverse(skc10))
    | ~ in(skc11,relation_dom(skc10))
    | ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11)
    | ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11) ),
    inference(spl,[status(thm),theory(equality)],[70,65]),
    [iquote('0:SpL:70.5,65.1')] ).

cnf(488,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ relation(function_inverse(skc10))
    | ~ function(function_inverse(skc10))
    | ~ in(skc11,relation_dom(skc10))
    | ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11) ),
    inference(obv,[status(thm),theory(equality)],[485]),
    [iquote('0:Obv:485.5')] ).

cnf(489,plain,
    ( ~ in(skc11,relation_dom(skc10))
    | ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11) ),
    inference(ssi,[status(thm)],[488,143,142,1,2,3]),
    [iquote('0:SSi:488.3,488.2,488.1,488.0,143.0,142.0,143.0,142.0,1.0,2.0,3.0,1.0,2.0,3.0')] ).

cnf(490,plain,
    ~ equal(apply(function_inverse(skc10),apply(skc10,skc11)),skc11),
    inference(mrr,[status(thm)],[489,28]),
    [iquote('0:MRR:489.0,28.0')] ).

cnf(551,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ one_to_one(v)
    | ~ function(v)
    | ~ relation(v)
    | ~ in(w,relation_dom(v))
    | ~ equal(u,function_inverse(v))
    | equal(apply(u,apply(v,w)),w) ),
    inference(eqr,[status(thm),theory(equality)],[72]),
    [iquote('0:EqR:72.7')] ).

cnf(1192,plain,
    ( ~ function(function_inverse(skc10))
    | ~ relation(function_inverse(skc10))
    | ~ one_to_one(skc10)
    | ~ function(skc10)
    | ~ relation(skc10)
    | ~ in(skc11,relation_dom(skc10))
    | ~ equal(function_inverse(skc10),function_inverse(skc10))
    | ~ equal(skc11,skc11) ),
    inference(spl,[status(thm),theory(equality)],[551,490]),
    [iquote('0:SpL:551.7,490.0')] ).

cnf(1197,plain,
    ( ~ function(function_inverse(skc10))
    | ~ relation(function_inverse(skc10))
    | ~ one_to_one(skc10)
    | ~ function(skc10)
    | ~ relation(skc10)
    | ~ in(skc11,relation_dom(skc10)) ),
    inference(obv,[status(thm),theory(equality)],[1192]),
    [iquote('0:Obv:1192.7')] ).

cnf(1198,plain,
    ~ in(skc11,relation_dom(skc10)),
    inference(ssi,[status(thm)],[1197,1,2,3,143,142]),
    [iquote('0:SSi:1197.4,1197.3,1197.2,1197.1,1197.0,1.0,2.0,3.0,1.0,2.0,3.0,1.0,2.0,3.0,143.0,142.0,143.0,142.0')] ).

cnf(1199,plain,
    $false,
    inference(mrr,[status(thm)],[1198,28]),
    [iquote('0:MRR:1198.0,28.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n020.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 23:02:48 EDT 2022
% 0.12/0.35  % CPUTime  : 
% 0.47/0.64  
% 0.47/0.64  SPASS V 3.9 
% 0.47/0.64  SPASS beiseite: Proof found.
% 0.47/0.64  % SZS status Theorem
% 0.47/0.64  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.47/0.64  SPASS derived 949 clauses, backtracked 0 clauses, performed 1 splits and kept 557 clauses.
% 0.47/0.64  SPASS allocated 98881 KBytes.
% 0.47/0.64  SPASS spent	0:00:00.28 on the problem.
% 0.47/0.64  		0:00:00.03 for the input.
% 0.47/0.64  		0:00:00.05 for the FLOTTER CNF translation.
% 0.47/0.64  		0:00:00.02 for inferences.
% 0.47/0.64  		0:00:00.00 for the backtracking.
% 0.47/0.64  		0:00:00.14 for the reduction.
% 0.47/0.64  
% 0.47/0.64  
% 0.47/0.64  Here is a proof with depth 2, length 22 :
% 0.47/0.64  % SZS output start Refutation
% See solution above
% 0.47/0.64  Formulae used in the proof : t56_funct_1 dt_k2_funct_1 t23_funct_1 t54_funct_1
% 0.47/0.64  
%------------------------------------------------------------------------------