TSTP Solution File: SEU215+3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 14:35:05 EDT 2022

% Result   : Theorem 13.68s 13.92s
% Output   : Refutation 13.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   34 (   9 unt;   9 nHn;  34 RR)
%            Number of literals    :  121 (   0 equ;  80 neg)
%            Maximal clause size   :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    function(skc10),
    file('SEU215+3.p',unknown),
    [] ).

cnf(2,axiom,
    relation(skc10),
    file('SEU215+3.p',unknown),
    [] ).

cnf(3,axiom,
    function(skc9),
    file('SEU215+3.p',unknown),
    [] ).

cnf(4,axiom,
    relation(skc9),
    file('SEU215+3.p',unknown),
    [] ).

cnf(23,axiom,
    in(skc11,relation_dom(skc9)),
    file('SEU215+3.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ relation(u)
    | ~ relation(v)
    | relation(relation_composition(v,u)) ),
    file('SEU215+3.p',unknown),
    [] ).

cnf(52,axiom,
    ~ equal(apply(relation_composition(skc9,skc10),skc11),apply(skc10,apply(skc9,skc11))),
    file('SEU215+3.p',unknown),
    [] ).

cnf(56,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ function(v)
    | ~ relation(v)
    | function(relation_composition(v,u)) ),
    file('SEU215+3.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(v,empty_set)
    | in(w,relation_dom(u))
    | equal(v,apply(u,w)) ),
    file('SEU215+3.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ relation(v)
    | ~ function(v)
    | ~ in(w,relation_dom(relation_composition(v,u)))
    | equal(apply(relation_composition(v,u),w),apply(u,apply(v,w))) ),
    file('SEU215+3.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ relation(u)
    | ~ function(u)
    | ~ relation(v)
    | ~ function(v)
    | ~ in(w,relation_dom(v))
    | ~ in(apply(v,w),relation_dom(u))
    | in(w,relation_dom(relation_composition(v,u))) ),
    file('SEU215+3.p',unknown),
    [] ).

cnf(74,plain,
    ( ~ function(skc9)
    | ~ function(u)
    | ~ relation(u)
    | function(relation_composition(skc9,u)) ),
    inference(res,[status(thm),theory(equality)],[4,56]),
    [iquote('0:Res:4.0,56.0')] ).

cnf(75,plain,
    ( ~ relation(u)
    | relation(relation_composition(skc9,u)) ),
    inference(res,[status(thm),theory(equality)],[4,47]),
    [iquote('0:Res:4.0,47.0')] ).

cnf(87,plain,
    ( ~ relation(skc9)
    | ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_dom(skc9))
    | ~ in(apply(skc9,v),relation_dom(u))
    | in(v,relation_dom(relation_composition(skc9,u))) ),
    inference(res,[status(thm),theory(equality)],[3,64]),
    [iquote('0:Res:3.0,64.0')] ).

cnf(88,plain,
    ( ~ relation(skc9)
    | ~ function(u)
    | ~ relation(u)
    | ~ in(v,relation_dom(relation_composition(skc9,u)))
    | equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
    inference(res,[status(thm),theory(equality)],[3,63]),
    [iquote('0:Res:3.0,63.0')] ).

cnf(132,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ relation(skc10)
    | ~ in(v,relation_dom(relation_composition(u,skc10)))
    | equal(apply(relation_composition(u,skc10),v),apply(skc10,apply(u,v))) ),
    inference(res,[status(thm),theory(equality)],[1,63]),
    [iquote('0:Res:1.0,63.2')] ).

cnf(136,plain,
    ( ~ relation(u)
    | ~ function(u)
    | function(relation_composition(skc9,u)) ),
    inference(mrr,[status(thm)],[74,3]),
    [iquote('0:MRR:74.0,3.0')] ).

cnf(156,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_dom(relation_composition(u,skc10)))
    | equal(apply(relation_composition(u,skc10),v),apply(skc10,apply(u,v))) ),
    inference(mrr,[status(thm)],[132,2]),
    [iquote('0:MRR:132.2,2.0')] ).

cnf(162,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_dom(relation_composition(skc9,u)))
    | equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
    inference(mrr,[status(thm)],[88,4]),
    [iquote('0:MRR:88.0,4.0')] ).

cnf(163,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_dom(skc9))
    | ~ in(apply(skc9,v),relation_dom(u))
    | in(v,relation_dom(relation_composition(skc9,u))) ),
    inference(mrr,[status(thm)],[87,4]),
    [iquote('0:MRR:87.0,4.0')] ).

cnf(406,plain,
    ( ~ function(u)
    | ~ relation(u)
    | in(v,relation_dom(u))
    | equal(apply(u,v),empty_set) ),
    inference(eqr,[status(thm),theory(equality)],[58]),
    [iquote('0:EqR:58.2')] ).

cnf(1469,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_dom(skc9))
    | equal(apply(u,apply(skc9,v)),empty_set)
    | in(v,relation_dom(relation_composition(skc9,u))) ),
    inference(res,[status(thm),theory(equality)],[406,163]),
    [iquote('0:Res:406.2,163.3')] ).

cnf(1471,plain,
    ( ~ relation(u)
    | ~ function(u)
    | ~ in(v,relation_dom(skc9))
    | equal(apply(u,apply(skc9,v)),empty_set)
    | in(v,relation_dom(relation_composition(skc9,u))) ),
    inference(obv,[status(thm),theory(equality)],[1469]),
    [iquote('0:Obv:1469.1')] ).

cnf(1505,plain,
    ( ~ function(relation_composition(skc9,u))
    | ~ relation(relation_composition(skc9,u))
    | ~ relation(u)
    | ~ function(u)
    | equal(apply(relation_composition(skc9,u),v),empty_set)
    | equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
    inference(res,[status(thm),theory(equality)],[406,162]),
    [iquote('0:Res:406.2,162.2')] ).

cnf(1510,plain,
    ( ~ relation(u)
    | ~ function(u)
    | equal(apply(relation_composition(skc9,u),v),empty_set)
    | equal(apply(relation_composition(skc9,u),v),apply(u,apply(skc9,v))) ),
    inference(ssi,[status(thm)],[1505,75,136]),
    [iquote('0:SSi:1505.1,1505.0,75.2,136.1,75.2,136.1')] ).

cnf(3816,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ relation(skc9)
    | ~ function(skc9)
    | ~ in(u,relation_dom(skc9))
    | equal(apply(skc10,apply(skc9,u)),empty_set)
    | equal(apply(relation_composition(skc9,skc10),u),apply(skc10,apply(skc9,u))) ),
    inference(res,[status(thm),theory(equality)],[1471,156]),
    [iquote('0:Res:1471.4,156.2')] ).

cnf(3827,plain,
    ( ~ in(u,relation_dom(skc9))
    | equal(apply(skc10,apply(skc9,u)),empty_set)
    | equal(apply(relation_composition(skc9,skc10),u),apply(skc10,apply(skc9,u))) ),
    inference(ssi,[status(thm)],[3816,3,4,1,2]),
    [iquote('0:SSi:3816.3,3816.2,3816.1,3816.0,3.0,4.0,3.0,4.0,1.0,2.0,1.0,2.0')] ).

cnf(3910,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | ~ equal(apply(skc10,apply(skc9,skc11)),apply(skc10,apply(skc9,skc11)))
    | equal(apply(relation_composition(skc9,skc10),skc11),empty_set) ),
    inference(spl,[status(thm),theory(equality)],[1510,52]),
    [iquote('0:SpL:1510.3,52.0')] ).

cnf(3915,plain,
    ( ~ relation(skc10)
    | ~ function(skc10)
    | equal(apply(relation_composition(skc9,skc10),skc11),empty_set) ),
    inference(obv,[status(thm),theory(equality)],[3910]),
    [iquote('0:Obv:3910.2')] ).

cnf(3916,plain,
    equal(apply(relation_composition(skc9,skc10),skc11),empty_set),
    inference(ssi,[status(thm)],[3915,1,2]),
    [iquote('0:SSi:3915.1,3915.0,1.0,2.0,1.0,2.0')] ).

cnf(3917,plain,
    ~ equal(apply(skc10,apply(skc9,skc11)),empty_set),
    inference(rew,[status(thm),theory(equality)],[3916,52]),
    [iquote('0:Rew:3916.0,52.0')] ).

cnf(11971,plain,
    ( ~ in(skc11,relation_dom(skc9))
    | equal(apply(skc10,apply(skc9,skc11)),empty_set)
    | equal(apply(skc10,apply(skc9,skc11)),empty_set) ),
    inference(spr,[status(thm),theory(equality)],[3827,3916]),
    [iquote('0:SpR:3827.2,3916.0')] ).

cnf(11991,plain,
    ( ~ in(skc11,relation_dom(skc9))
    | equal(apply(skc10,apply(skc9,skc11)),empty_set) ),
    inference(obv,[status(thm),theory(equality)],[11971]),
    [iquote('0:Obv:11971.1')] ).

cnf(11992,plain,
    $false,
    inference(mrr,[status(thm)],[11991,23,3917]),
    [iquote('0:MRR:11991.0,11991.1,23.0,3917.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n017.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun 19 10:03:28 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 13.68/13.92  
% 13.68/13.92  SPASS V 3.9 
% 13.68/13.92  SPASS beiseite: Proof found.
% 13.68/13.92  % SZS status Theorem
% 13.68/13.92  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 13.68/13.92  SPASS derived 9131 clauses, backtracked 0 clauses, performed 2 splits and kept 4738 clauses.
% 13.68/13.92  SPASS allocated 116102 KBytes.
% 13.68/13.92  SPASS spent	0:0:12.92 on the problem.
% 13.68/13.92  		0:00:00.04 for the input.
% 13.68/13.92  		0:00:00.03 for the FLOTTER CNF translation.
% 13.68/13.92  		0:00:00.15 for inferences.
% 13.68/13.92  		0:00:00.02 for the backtracking.
% 13.68/13.92  		0:0:12.57 for the reduction.
% 13.68/13.92  
% 13.68/13.92  
% 13.68/13.92  Here is a proof with depth 4, length 34 :
% 13.68/13.92  % SZS output start Refutation
% See solution above
% 13.68/13.92  Formulae used in the proof : t23_funct_1 dt_k5_relat_1 fc1_funct_1 d4_funct_1 t22_funct_1 t21_funct_1
% 13.68/13.92  
%------------------------------------------------------------------------------