TSTP Solution File: FLD018-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD018-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 : Sat Jul 16 02:28:19 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   18 (   6 unt;   0 nHn;  18 RR)
%            Number of literals    :   34 (   0 equ;  21 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    defined(a),
    file('FLD018-3.p',unknown),
    [] ).

cnf(2,axiom,
    sum__dfg(additive_identity,a,additive_identity),
    file('FLD018-3.p',unknown),
    [] ).

cnf(3,axiom,
    ~ sum__dfg(additive_identity,additive_inverse(a),additive_identity),
    file('FLD018-3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,y,v)
    | ~ sum__dfg(u,x,z)
    | sum__dfg(z,y,w) ),
    file('FLD018-3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,u) ),
    file('FLD018-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_inverse(u),u,additive_identity) ),
    file('FLD018-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ sum__dfg(u,v,w)
    | sum__dfg(v,u,w) ),
    file('FLD018-3.p',unknown),
    [] ).

cnf(35,plain,
    ( ~ sum__dfg(u,v,a)
    | ~ sum__dfg(additive_identity,u,w)
    | sum__dfg(w,v,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[2,5]),
    [iquote('0:Res:2.0,5.2')] ).

cnf(47,plain,
    ( ~ sum__dfg(u,v,additive_identity)
    | ~ sum__dfg(u,w,additive_identity)
    | ~ sum__dfg(w,additive_inverse(a),v) ),
    inference(res,[status(thm),theory(equality)],[5,3]),
    [iquote('0:Res:5.3,3.0')] ).

cnf(50,plain,
    ( ~ sum__dfg(a,u,a)
    | sum__dfg(additive_identity,u,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[2,35]),
    [iquote('0:Res:2.0,35.0')] ).

cnf(58,plain,
    ( ~ sum__dfg(additive_identity,u,additive_identity)
    | ~ sum__dfg(a,additive_inverse(a),u) ),
    inference(res,[status(thm),theory(equality)],[2,47]),
    [iquote('0:Res:2.0,47.0')] ).

cnf(75,plain,
    ( ~ defined(u)
    | sum__dfg(u,additive_identity,u) ),
    inference(res,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Res:6.1,8.0')] ).

cnf(77,plain,
    ( ~ defined(u)
    | sum__dfg(u,additive_inverse(u),additive_identity) ),
    inference(res,[status(thm),theory(equality)],[7,8]),
    [iquote('0:Res:7.1,8.0')] ).

cnf(78,plain,
    ( ~ defined(a)
    | sum__dfg(additive_identity,additive_identity,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[75,50]),
    [iquote('0:Res:75.1,50.0')] ).

cnf(80,plain,
    sum__dfg(additive_identity,additive_identity,additive_identity),
    inference(ssi,[status(thm)],[78,1]),
    [iquote('0:SSi:78.0,1.0')] ).

cnf(88,plain,
    ( ~ defined(a)
    | ~ sum__dfg(additive_identity,additive_identity,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[77,58]),
    [iquote('0:Res:77.1,58.1')] ).

cnf(89,plain,
    ~ sum__dfg(additive_identity,additive_identity,additive_identity),
    inference(ssi,[status(thm)],[88,1]),
    [iquote('0:SSi:88.0,1.0')] ).

cnf(90,plain,
    $false,
    inference(mrr,[status(thm)],[89,80]),
    [iquote('0:MRR:89.0,80.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : FLD018-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun  6 23:03:36 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 47 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.19/0.42  SPASS allocated 75672 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 3, length 18 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : a_is_defined sum_2 not_sum_3 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition
% 0.19/0.42  
%------------------------------------------------------------------------------