TSTP Solution File: FLD005-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD005-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 02:28:13 EDT 2022

% Result   : Unsatisfiable 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   17 (   4 unt;   0 nHn;  17 RR)
%            Number of literals    :   39 (   0 equ;  29 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    defined(a),
    file('FLD005-3.p',unknown),
    [] ).

cnf(2,axiom,
    defined(b),
    file('FLD005-3.p',unknown),
    [] ).

cnf(3,axiom,
    ~ sum__dfg(a,u,b),
    file('FLD005-3.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,v,y)
    | ~ sum__dfg(z,x,u)
    | sum__dfg(z,y,w) ),
    file('FLD005-3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,u) ),
    file('FLD005-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_inverse(u),u,additive_identity) ),
    file('FLD005-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ sum__dfg(u,v,w)
    | sum__dfg(v,u,w) ),
    file('FLD005-3.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ defined(u)
    | defined(additive_inverse(u)) ),
    file('FLD005-3.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ defined(u)
    | ~ defined(v)
    | sum__dfg(v,u,add(v,u)) ),
    file('FLD005-3.p',unknown),
    [] ).

cnf(31,plain,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,v,b)
    | ~ sum__dfg(a,u,x) ),
    inference(res,[status(thm),theory(equality)],[4,3]),
    [iquote('0:Res:4.3,3.0')] ).

cnf(45,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(65,plain,
    ( ~ defined(u)
    | ~ defined(v)
    | ~ sum__dfg(w,u,b)
    | ~ sum__dfg(a,v,w) ),
    inference(res,[status(thm),theory(equality)],[22,31]),
    [iquote('0:Res:22.2,31.0')] ).

cnf(162,plain,
    ( ~ defined(b)
    | ~ defined(b)
    | ~ defined(u)
    | ~ sum__dfg(a,u,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[6,65]),
    [iquote('0:Res:6.1,65.2')] ).

cnf(165,plain,
    ( ~ defined(b)
    | ~ defined(u)
    | ~ sum__dfg(a,u,additive_identity) ),
    inference(obv,[status(thm),theory(equality)],[162]),
    [iquote('0:Obv:162.0')] ).

cnf(166,plain,
    ( ~ defined(u)
    | ~ sum__dfg(a,u,additive_identity) ),
    inference(ssi,[status(thm)],[165,2]),
    [iquote('0:SSi:165.0,2.0')] ).

cnf(167,plain,
    ( ~ defined(a)
    | ~ defined(additive_inverse(a)) ),
    inference(res,[status(thm),theory(equality)],[45,166]),
    [iquote('0:Res:45.1,166.1')] ).

cnf(169,plain,
    $false,
    inference(ssi,[status(thm)],[167,18,1]),
    [iquote('0:SSi:167.1,167.0,18.0,1.0,1.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : FLD005-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n028.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun  6 11:21:58 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.45  
% 0.20/0.45  SPASS V 3.9 
% 0.20/0.45  SPASS beiseite: Proof found.
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.45  SPASS derived 109 clauses, backtracked 0 clauses, performed 0 splits and kept 105 clauses.
% 0.20/0.45  SPASS allocated 75767 KBytes.
% 0.20/0.45  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.45  		0:00:00.03 for the input.
% 0.20/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45  		0:00:00.00 for inferences.
% 0.20/0.45  		0:00:00.00 for the backtracking.
% 0.20/0.45  		0:00:00.02 for the reduction.
% 0.20/0.45  
% 0.20/0.45  
% 0.20/0.45  Here is a proof with depth 4, length 17 :
% 0.20/0.45  % SZS output start Refutation
% See solution above
% 0.20/0.45  Formulae used in the proof : a_is_defined b_is_defined not_sum_3 associativity_addition_1 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_inverse totality_of_addition
% 0.20/0.45  
%------------------------------------------------------------------------------