TSTP Solution File: FLD007-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD007-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 02:28:14 EDT 2022

% Result   : Unsatisfiable 0.22s 0.45s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (   5 unt;   0 nHn;  16 RR)
%            Number of literals    :   31 (   0 equ;  22 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   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('FLD007-3.p',unknown),
    [] ).

cnf(2,axiom,
    ~ sum__dfg(additive_identity,additive_inverse(additive_inverse(a)),a),
    file('FLD007-3.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,y,v)
    | ~ sum__dfg(u,x,z)
    | sum__dfg(z,y,w) ),
    file('FLD007-3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,u) ),
    file('FLD007-3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_inverse(u),u,additive_identity) ),
    file('FLD007-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ sum__dfg(u,v,w)
    | sum__dfg(v,u,w) ),
    file('FLD007-3.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ defined(u)
    | defined(additive_inverse(u)) ),
    file('FLD007-3.p',unknown),
    [] ).

cnf(32,plain,
    ( ~ sum__dfg(u,v,a)
    | ~ sum__dfg(u,w,additive_identity)
    | ~ sum__dfg(w,additive_inverse(additive_inverse(a)),v) ),
    inference(res,[status(thm),theory(equality)],[4,2]),
    [iquote('0:Res:4.3,2.0')] ).

cnf(43,plain,
    ( ~ defined(u)
    | sum__dfg(u,additive_identity,u) ),
    inference(res,[status(thm),theory(equality)],[5,7]),
    [iquote('0:Res:5.1,7.0')] ).

cnf(44,plain,
    ( ~ defined(u)
    | sum__dfg(u,additive_inverse(u),additive_identity) ),
    inference(res,[status(thm),theory(equality)],[6,7]),
    [iquote('0:Res:6.1,7.0')] ).

cnf(81,plain,
    ( ~ defined(additive_inverse(a))
    | ~ sum__dfg(u,additive_identity,a)
    | ~ sum__dfg(u,additive_inverse(a),additive_identity) ),
    inference(res,[status(thm),theory(equality)],[44,32]),
    [iquote('0:Res:44.1,32.2')] ).

cnf(84,plain,
    ( ~ sum__dfg(u,additive_identity,a)
    | ~ sum__dfg(u,additive_inverse(a),additive_identity) ),
    inference(ssi,[status(thm)],[81,17,1]),
    [iquote('0:SSi:81.0,17.0,1.1')] ).

cnf(100,plain,
    ( ~ defined(a)
    | ~ sum__dfg(a,additive_identity,a) ),
    inference(res,[status(thm),theory(equality)],[44,84]),
    [iquote('0:Res:44.1,84.1')] ).

cnf(101,plain,
    ~ sum__dfg(a,additive_identity,a),
    inference(ssi,[status(thm)],[100,1]),
    [iquote('0:SSi:100.0,1.0')] ).

cnf(103,plain,
    ~ defined(a),
    inference(res,[status(thm),theory(equality)],[43,101]),
    [iquote('0:Res:43.1,101.0')] ).

cnf(104,plain,
    $false,
    inference(ssi,[status(thm)],[103,1]),
    [iquote('0:SSi:103.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : FLD007-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Mon Jun  6 19:42:07 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.22/0.45  
% 0.22/0.45  SPASS V 3.9 
% 0.22/0.45  SPASS beiseite: Proof found.
% 0.22/0.45  % SZS status Theorem
% 0.22/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.22/0.45  SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 73 clauses.
% 0.22/0.45  SPASS allocated 75713 KBytes.
% 0.22/0.45  SPASS spent	0:00:00.07 on the problem.
% 0.22/0.45  		0:00:00.04 for the input.
% 0.22/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.45  		0:00:00.00 for inferences.
% 0.22/0.45  		0:00:00.00 for the backtracking.
% 0.22/0.45  		0:00:00.01 for the reduction.
% 0.22/0.45  
% 0.22/0.45  
% 0.22/0.45  Here is a proof with depth 4, length 16 :
% 0.22/0.45  % SZS output start Refutation
% See solution above
% 0.22/0.45  Formulae used in the proof : a_is_defined not_sum_2 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_inverse
% 0.22/0.45  
%------------------------------------------------------------------------------