TSTP Solution File: SEU025+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU025+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 0.34s 0.53s
% Output   : Refutation 0.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   30 (  11 unt;   0 nHn;  30 RR)
%            Number of literals    :   66 (   0 equ;  39 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    relation(skc9),
    file('SEU025+1.p',unknown),
    [] ).

cnf(2,axiom,
    function(skc9),
    file('SEU025+1.p',unknown),
    [] ).

cnf(3,axiom,
    one_to_one(skc9),
    file('SEU025+1.p',unknown),
    [] ).

cnf(27,axiom,
    subset(u,u),
    file('SEU025+1.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | relation(function_inverse(u)) ),
    file('SEU025+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | function(function_inverse(u)) ),
    file('SEU025+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ one_to_one(u)
    | ~ function(u)
    | ~ relation(u)
    | equal(relation_dom(function_inverse(u)),relation_rng(u)) ),
    file('SEU025+1.p',unknown),
    [] ).

cnf(60,axiom,
    ( ~ one_to_one(u)
    | ~ function(u)
    | ~ relation(u)
    | equal(relation_rng(function_inverse(u)),relation_dom(u)) ),
    file('SEU025+1.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9))
    | ~ equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
    file('SEU025+1.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ relation(u)
    | ~ relation(v)
    | ~ subset(relation_rng(v),relation_dom(u))
    | equal(relation_dom(relation_composition(v,u)),relation_dom(v)) ),
    file('SEU025+1.p',unknown),
    [] ).

cnf(65,axiom,
    ( ~ relation(u)
    | ~ relation(v)
    | ~ subset(relation_dom(v),relation_rng(u))
    | equal(relation_rng(relation_composition(u,v)),relation_rng(v)) ),
    file('SEU025+1.p',unknown),
    [] ).

cnf(67,plain,
    ( ~ relation(skc9)
    | ~ function(skc9)
    | equal(relation_dom(function_inverse(skc9)),relation_rng(skc9)) ),
    inference(res,[status(thm),theory(equality)],[3,59]),
    [iquote('0:Res:3.0,59.2')] ).

cnf(68,plain,
    ( ~ relation(skc9)
    | ~ function(skc9)
    | equal(relation_rng(function_inverse(skc9)),relation_dom(skc9)) ),
    inference(res,[status(thm),theory(equality)],[3,60]),
    [iquote('0:Res:3.0,60.2')] ).

cnf(72,plain,
    ( ~ relation(skc9)
    | relation(function_inverse(skc9)) ),
    inference(res,[status(thm),theory(equality)],[2,45]),
    [iquote('0:Res:2.0,45.1')] ).

cnf(73,plain,
    ( ~ relation(skc9)
    | function(function_inverse(skc9)) ),
    inference(res,[status(thm),theory(equality)],[2,46]),
    [iquote('0:Res:2.0,46.1')] ).

cnf(75,plain,
    ( ~ relation(u)
    | ~ subset(relation_rng(skc9),relation_dom(u))
    | equal(relation_dom(relation_composition(skc9,u)),relation_dom(skc9)) ),
    inference(res,[status(thm),theory(equality)],[1,64]),
    [iquote('0:Res:1.0,64.0')] ).

cnf(86,plain,
    ( ~ relation(u)
    | ~ subset(relation_dom(u),relation_rng(skc9))
    | equal(relation_rng(relation_composition(skc9,u)),relation_rng(u)) ),
    inference(res,[status(thm),theory(equality)],[1,65]),
    [iquote('0:Res:1.0,65.1')] ).

cnf(93,plain,
    relation(function_inverse(skc9)),
    inference(mrr,[status(thm)],[72,1]),
    [iquote('0:MRR:72.0,1.0')] ).

cnf(94,plain,
    function(function_inverse(skc9)),
    inference(mrr,[status(thm)],[73,1]),
    [iquote('0:MRR:73.0,1.0')] ).

cnf(95,plain,
    equal(relation_dom(function_inverse(skc9)),relation_rng(skc9)),
    inference(mrr,[status(thm)],[67,1,2]),
    [iquote('0:MRR:67.0,67.1,1.0,2.0')] ).

cnf(96,plain,
    equal(relation_rng(function_inverse(skc9)),relation_dom(skc9)),
    inference(mrr,[status(thm)],[68,1,2]),
    [iquote('0:MRR:68.0,68.1,1.0,2.0')] ).

cnf(665,plain,
    ( ~ relation(function_inverse(skc9))
    | ~ subset(relation_rng(skc9),relation_rng(skc9))
    | equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
    inference(spl,[status(thm),theory(equality)],[95,75]),
    [iquote('0:SpL:95.0,75.1')] ).

cnf(671,plain,
    ( ~ subset(relation_rng(skc9),relation_rng(skc9))
    | equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
    inference(ssi,[status(thm)],[665,94,93]),
    [iquote('0:SSi:665.0,94.0,93.0')] ).

cnf(672,plain,
    equal(relation_dom(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)),
    inference(mrr,[status(thm)],[671,27]),
    [iquote('0:MRR:671.0,27.0')] ).

cnf(673,plain,
    ( ~ equal(relation_dom(skc9),relation_dom(skc9))
    | ~ equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
    inference(rew,[status(thm),theory(equality)],[672,63]),
    [iquote('0:Rew:672.0,63.0')] ).

cnf(674,plain,
    ~ equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)),
    inference(obv,[status(thm),theory(equality)],[673]),
    [iquote('0:Obv:673.0')] ).

cnf(741,plain,
    ( ~ relation(function_inverse(skc9))
    | ~ subset(relation_rng(skc9),relation_rng(skc9))
    | equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_rng(function_inverse(skc9))) ),
    inference(spl,[status(thm),theory(equality)],[95,86]),
    [iquote('0:SpL:95.0,86.1')] ).

cnf(750,plain,
    ( ~ relation(function_inverse(skc9))
    | ~ subset(relation_rng(skc9),relation_rng(skc9))
    | equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
    inference(rew,[status(thm),theory(equality)],[96,741]),
    [iquote('0:Rew:96.0,741.2')] ).

cnf(751,plain,
    ( ~ subset(relation_rng(skc9),relation_rng(skc9))
    | equal(relation_rng(relation_composition(skc9,function_inverse(skc9))),relation_dom(skc9)) ),
    inference(ssi,[status(thm)],[750,94,93]),
    [iquote('0:SSi:750.0,94.0,93.0')] ).

cnf(752,plain,
    $false,
    inference(mrr,[status(thm)],[751,27,674]),
    [iquote('0:MRR:751.0,751.1,27.0,674.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU025+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.36  % Computer : n003.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 600
% 0.13/0.36  % DateTime : Sun Jun 19 16:05:59 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.34/0.53  
% 0.34/0.53  SPASS V 3.9 
% 0.34/0.53  SPASS beiseite: Proof found.
% 0.34/0.53  % SZS status Theorem
% 0.34/0.53  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.34/0.53  SPASS derived 523 clauses, backtracked 0 clauses, performed 0 splits and kept 271 clauses.
% 0.34/0.53  SPASS allocated 98180 KBytes.
% 0.34/0.53  SPASS spent	0:00:00.16 on the problem.
% 0.34/0.53  		0:00:00.03 for the input.
% 0.34/0.53  		0:00:00.03 for the FLOTTER CNF translation.
% 0.34/0.53  		0:00:00.01 for inferences.
% 0.34/0.53  		0:00:00.00 for the backtracking.
% 0.34/0.53  		0:00:00.05 for the reduction.
% 0.34/0.53  
% 0.34/0.53  
% 0.34/0.53  Here is a proof with depth 2, length 30 :
% 0.34/0.53  % SZS output start Refutation
% See solution above
% 0.34/0.53  Formulae used in the proof : t58_funct_1 reflexivity_r1_tarski dt_k2_funct_1 t55_funct_1 t46_relat_1 t47_relat_1
% 0.34/0.53  
%------------------------------------------------------------------------------