TSTP Solution File: FLD016-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD016-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : Sat Jul 16 02:28:18 EDT 2022

% Result   : Unsatisfiable 0.21s 0.58s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   17 (   8 unt;   0 nHn;  17 RR)
%            Number of literals    :   33 (   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    :   12 (  12 usr;  11 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    defined(a),
    file('FLD016-3.p',unknown),
    [] ).

cnf(4,axiom,
    defined(v__dfg),
    file('FLD016-3.p',unknown),
    [] ).

cnf(5,axiom,
    sum__dfg(a,u__dfg,b),
    file('FLD016-3.p',unknown),
    [] ).

cnf(6,axiom,
    sum__dfg(a,v__dfg,b),
    file('FLD016-3.p',unknown),
    [] ).

cnf(7,axiom,
    ~ sum__dfg(additive_identity,u__dfg,v__dfg),
    file('FLD016-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,v,y)
    | ~ sum__dfg(z,x,u)
    | sum__dfg(z,y,w) ),
    file('FLD016-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,y,v)
    | ~ sum__dfg(u,x,z)
    | sum__dfg(z,y,w) ),
    file('FLD016-3.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,u) ),
    file('FLD016-3.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_inverse(u),u,additive_identity) ),
    file('FLD016-3.p',unknown),
    [] ).

cnf(41,plain,
    ( ~ sum__dfg(u,v__dfg,v)
    | ~ sum__dfg(w,a,u)
    | sum__dfg(w,b,v) ),
    inference(res,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Res:6.0,8.1')] ).

cnf(61,plain,
    ( ~ sum__dfg(u,v,v__dfg)
    | ~ sum__dfg(u,w,additive_identity)
    | ~ sum__dfg(w,u__dfg,v) ),
    inference(res,[status(thm),theory(equality)],[9,7]),
    [iquote('0:Res:9.3,7.0')] ).

cnf(70,plain,
    ( ~ sum__dfg(u,b,v__dfg)
    | ~ sum__dfg(u,a,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[5,61]),
    [iquote('0:Res:5.0,61.1')] ).

cnf(618,plain,
    ( ~ defined(v__dfg)
    | ~ sum__dfg(u,a,additive_identity)
    | sum__dfg(u,b,v__dfg) ),
    inference(res,[status(thm),theory(equality)],[10,41]),
    [iquote('0:Res:10.1,41.0')] ).

cnf(636,plain,
    ( ~ sum__dfg(u,a,additive_identity)
    | sum__dfg(u,b,v__dfg) ),
    inference(ssi,[status(thm)],[618,4]),
    [iquote('0:SSi:618.0,4.0')] ).

cnf(637,plain,
    ~ sum__dfg(u,a,additive_identity),
    inference(mrr,[status(thm)],[636,70]),
    [iquote('0:MRR:636.1,70.0')] ).

cnf(645,plain,
    ~ defined(a),
    inference(res,[status(thm),theory(equality)],[11,637]),
    [iquote('0:Res:11.1,637.0')] ).

cnf(647,plain,
    $false,
    inference(ssi,[status(thm)],[645,1]),
    [iquote('0:SSi:645.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : FLD016-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jun  6 20:18:46 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  
% 0.21/0.58  SPASS V 3.9 
% 0.21/0.58  SPASS beiseite: Proof found.
% 0.21/0.58  % SZS status Theorem
% 0.21/0.58  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.58  SPASS derived 538 clauses, backtracked 13 clauses, performed 2 splits and kept 491 clauses.
% 0.21/0.58  SPASS allocated 76181 KBytes.
% 0.21/0.58  SPASS spent	0:00:00.21 on the problem.
% 0.21/0.58  		0:00:00.04 for the input.
% 0.21/0.58  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.58  		0:00:00.01 for inferences.
% 0.21/0.58  		0:00:00.00 for the backtracking.
% 0.21/0.58  		0:00:00.14 for the reduction.
% 0.21/0.58  
% 0.21/0.58  
% 0.21/0.58  Here is a proof with depth 3, length 17 :
% 0.21/0.58  % SZS output start Refutation
% See solution above
% 0.21/0.58  Formulae used in the proof : a_is_defined v_is_defined sum_5 sum_6 not_sum_7 associativity_addition_1 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition
% 0.21/0.58  
%------------------------------------------------------------------------------