TSTP Solution File: SEU220+3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU220+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 14:35:10 EDT 2022

% Result   : Theorem 1.65s 1.88s
% Output   : Refutation 1.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   28 (  10 unt;   0 nHn;  28 RR)
%            Number of literals    :   98 (   0 equ;  79 neg)
%            Maximal clause size   :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    one_to_one(skc10),
    file('SEU220+3.p',unknown),
    [] ).

cnf(2,axiom,
    function(skc10),
    file('SEU220+3.p',unknown),
    [] ).

cnf(3,axiom,
    relation(skc10),
    file('SEU220+3.p',unknown),
    [] ).

cnf(28,axiom,
    in(skc11,relation_rng(skc10)),
    file('SEU220+3.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | relation(function_inverse(u)) ),
    file('SEU220+3.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | function(function_inverse(u)) ),
    file('SEU220+3.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ one_to_one(u)
    | ~ function(u)
    | ~ relation(u)
    | equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
    file('SEU220+3.p',unknown),
    [] ).

cnf(67,axiom,
    ( ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11)
    | ~ equal(apply(relation_composition(function_inverse(skc10),skc10),skc11),skc11) ),
    file('SEU220+3.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ in(u,relation_rng(v))
    | ~ equal(w,apply(x,u))
    | ~ skP0(x,w,v,u)
    | equal(u,apply(v,w)) ),
    file('SEU220+3.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ one_to_one(v)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(u,function_inverse(v))
    | skP0(u,w,v,x) ),
    file('SEU220+3.p',unknown),
    [] ).

cnf(72,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('SEU220+3.p',unknown),
    [] ).

cnf(88,plain,
    ( ~ function(skc10)
    | ~ one_to_one(skc10)
    | equal(relation_dom(function_inverse(skc10)),relation_rng(skc10)) ),
    inference(res,[status(thm),theory(equality)],[3,62]),
    [iquote('0:Res:3.0,62.0')] ).

cnf(91,plain,
    ( ~ function(skc10)
    | relation(function_inverse(skc10)) ),
    inference(res,[status(thm),theory(equality)],[3,46]),
    [iquote('0:Res:3.0,46.0')] ).

cnf(92,plain,
    ( ~ function(skc10)
    | function(function_inverse(skc10)) ),
    inference(res,[status(thm),theory(equality)],[3,47]),
    [iquote('0:Res:3.0,47.0')] ).

cnf(148,plain,
    relation(function_inverse(skc10)),
    inference(mrr,[status(thm)],[91,2]),
    [iquote('0:MRR:91.0,2.0')] ).

cnf(149,plain,
    function(function_inverse(skc10)),
    inference(mrr,[status(thm)],[92,2]),
    [iquote('0:MRR:92.0,2.0')] ).

cnf(150,plain,
    equal(relation_dom(function_inverse(skc10)),relation_rng(skc10)),
    inference(mrr,[status(thm)],[88,2,1]),
    [iquote('0:MRR:88.0,88.1,2.0,1.0')] ).

cnf(580,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ one_to_one(v)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(u,function_inverse(v))
    | ~ in(w,relation_rng(v))
    | ~ equal(x,apply(u,w))
    | equal(w,apply(v,x)) ),
    inference(res,[status(thm),theory(equality)],[70,69]),
    [iquote('0:Res:70.6,69.2')] ).

cnf(615,plain,
    ( ~ relation(function_inverse(skc10))
    | ~ function(function_inverse(skc10))
    | ~ relation(skc10)
    | ~ function(skc10)
    | ~ in(skc11,relation_dom(function_inverse(skc10)))
    | ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11)
    | ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
    inference(spl,[status(thm),theory(equality)],[72,67]),
    [iquote('0:SpL:72.5,67.1')] ).

cnf(622,plain,
    ( ~ relation(function_inverse(skc10))
    | ~ function(function_inverse(skc10))
    | ~ relation(skc10)
    | ~ function(skc10)
    | ~ in(skc11,relation_dom(function_inverse(skc10)))
    | ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
    inference(obv,[status(thm),theory(equality)],[615]),
    [iquote('0:Obv:615.5')] ).

cnf(623,plain,
    ( ~ relation(function_inverse(skc10))
    | ~ function(function_inverse(skc10))
    | ~ relation(skc10)
    | ~ function(skc10)
    | ~ in(skc11,relation_rng(skc10))
    | ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
    inference(rew,[status(thm),theory(equality)],[150,622]),
    [iquote('0:Rew:150.0,622.4')] ).

cnf(624,plain,
    ( ~ in(skc11,relation_rng(skc10))
    | ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11) ),
    inference(ssi,[status(thm)],[623,1,2,3,149,148]),
    [iquote('0:SSi:623.3,623.2,623.1,623.0,1.0,2.0,3.0,1.0,2.0,3.0,149.0,148.0,149.0,148.0')] ).

cnf(625,plain,
    ~ equal(apply(skc10,apply(function_inverse(skc10),skc11)),skc11),
    inference(mrr,[status(thm)],[624,28]),
    [iquote('0:MRR:624.0,28.0')] ).

cnf(1714,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ one_to_one(v)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(u,function_inverse(v))
    | ~ in(w,relation_rng(v))
    | equal(apply(v,apply(u,w)),w) ),
    inference(eqr,[status(thm),theory(equality)],[580]),
    [iquote('0:EqR:580.7')] ).

cnf(4432,plain,
    ( ~ function(function_inverse(skc10))
    | ~ relation(function_inverse(skc10))
    | ~ one_to_one(skc10)
    | ~ function(skc10)
    | ~ relation(skc10)
    | ~ equal(function_inverse(skc10),function_inverse(skc10))
    | ~ in(skc11,relation_rng(skc10))
    | ~ equal(skc11,skc11) ),
    inference(spl,[status(thm),theory(equality)],[1714,625]),
    [iquote('0:SpL:1714.7,625.0')] ).

cnf(4443,plain,
    ( ~ function(function_inverse(skc10))
    | ~ relation(function_inverse(skc10))
    | ~ one_to_one(skc10)
    | ~ function(skc10)
    | ~ relation(skc10)
    | ~ in(skc11,relation_rng(skc10)) ),
    inference(obv,[status(thm),theory(equality)],[4432]),
    [iquote('0:Obv:4432.7')] ).

cnf(4444,plain,
    ~ in(skc11,relation_rng(skc10)),
    inference(ssi,[status(thm)],[4443,1,2,3,149,148]),
    [iquote('0:SSi:4443.4,4443.3,4443.2,4443.1,4443.0,1.0,2.0,3.0,1.0,2.0,3.0,1.0,2.0,3.0,149.0,148.0,149.0,148.0')] ).

cnf(4445,plain,
    $false,
    inference(mrr,[status(thm)],[4444,28]),
    [iquote('0:MRR:4444.0,28.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU220+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n019.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 03:15:09 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.65/1.88  
% 1.65/1.88  SPASS V 3.9 
% 1.65/1.88  SPASS beiseite: Proof found.
% 1.65/1.88  % SZS status Theorem
% 1.65/1.88  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.65/1.88  SPASS derived 3453 clauses, backtracked 0 clauses, performed 1 splits and kept 1804 clauses.
% 1.65/1.88  SPASS allocated 102681 KBytes.
% 1.65/1.88  SPASS spent	0:00:01.45 on the problem.
% 1.65/1.88  		0:00:00.03 for the input.
% 1.65/1.88  		0:00:00.05 for the FLOTTER CNF translation.
% 1.65/1.88  		0:00:00.06 for inferences.
% 1.65/1.88  		0:00:00.00 for the backtracking.
% 1.65/1.88  		0:00:01.25 for the reduction.
% 1.65/1.88  
% 1.65/1.88  
% 1.65/1.88  Here is a proof with depth 3, length 28 :
% 1.65/1.88  % SZS output start Refutation
% See solution above
% 1.65/1.88  Formulae used in the proof : t57_funct_1 dt_k2_funct_1 t55_funct_1 t54_funct_1 t23_funct_1
% 1.65/1.88  
%------------------------------------------------------------------------------