%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : FLD023-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.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 02:28:20 EDT 2022

% Result   : Unsatisfiable 0.15s 0.36s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   15 (   7 unt;   0 nHn;  15 RR)
%            Number of literals    :   26 (   0 equ;  17 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    :   10 (  10 usr;   9 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    defined(a),
    file('FLD023-3.p',unknown),
    [] ).

cnf(3,axiom,
    sum__dfg(additive_identity,a,b),
    file('FLD023-3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ sum__dfg(b,additive_inverse(a),additive_identity),
    file('FLD023-3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,y,v)
    | ~ sum__dfg(u,x,z)
    | sum__dfg(z,y,w) ),
    file('FLD023-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_identity,u,u) ),
    file('FLD023-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ defined(u)
    | sum__dfg(additive_inverse(u),u,additive_identity) ),
    file('FLD023-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sum__dfg(u,v,w)
    | sum__dfg(v,u,w) ),
    file('FLD023-3.p',unknown),
    [] ).

cnf(18,axiom,
    defined(additive_identity),
    file('FLD023-3.p',unknown),
    [] ).

cnf(45,plain,
    ( ~ sum__dfg(u,v,additive_identity)
    | ~ sum__dfg(u,w,b)
    | ~ sum__dfg(w,additive_inverse(a),v) ),
    inference(res,[status(thm),theory(equality)],[6,4]),
    [iquote('0:Res:6.3,4.0')] ).

cnf(53,plain,
    ( ~ sum__dfg(additive_identity,u,additive_identity)
    | ~ sum__dfg(a,additive_inverse(a),u) ),
    inference(res,[status(thm),theory(equality)],[3,45]),
    [iquote('0:Res:3.0,45.0')] ).

cnf(73,plain,
    ( ~ defined(u)
    | sum__dfg(u,additive_inverse(u),additive_identity) ),
    inference(res,[status(thm),theory(equality)],[8,9]),
    [iquote('0:Res:8.1,9.0')] ).

cnf(92,plain,
    ( ~ defined(a)
    | ~ sum__dfg(additive_identity,additive_identity,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[73,53]),
    [iquote('0:Res:73.1,53.1')] ).

cnf(93,plain,
    ~ sum__dfg(additive_identity,additive_identity,additive_identity),
    inference(ssi,[status(thm)],[92,1]),
    [iquote('0:SSi:92.0,1.0')] ).

cnf(94,plain,
    ~ defined(additive_identity),
    inference(res,[status(thm),theory(equality)],[7,93]),
    [iquote('0:Res:7.1,93.0')] ).

cnf(98,plain,
    $false,
    inference(ssi,[status(thm)],[94,18]),
    [iquote('0:SSi:94.0,18.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : FLD023-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.02/0.11  % Command  : run_spass %d %s
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit : 300
% 0.11/0.30  % WCLimit  : 600
% 0.11/0.30  % DateTime : Mon Jun  6 23:38:05 EDT 2022
% 0.11/0.30  % CPUTime  : 
% 0.15/0.36  
% 0.15/0.36  SPASS V 3.9 
% 0.15/0.36  SPASS beiseite: Proof found.
% 0.15/0.36  % SZS status Theorem
% 0.15/0.36  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.15/0.36  SPASS derived 56 clauses, backtracked 0 clauses, performed 0 splits and kept 66 clauses.
% 0.15/0.36  SPASS allocated 75683 KBytes.
% 0.15/0.36  SPASS spent	0:00:00.05 on the problem.
% 0.15/0.36  		0:00:00.03 for the input.
% 0.15/0.36  		0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.36  		0:00:00.00 for inferences.
% 0.15/0.36  		0:00:00.00 for the backtracking.
% 0.15/0.36  		0:00:00.00 for the reduction.
% 0.15/0.36  
% 0.15/0.36  
% 0.15/0.36  Here is a proof with depth 4, length 15 :
% 0.15/0.36  % SZS output start Refutation
% See solution above
% 0.15/0.36  Formulae used in the proof : a_is_defined sum_3 not_sum_4 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_identity
% 0.15/0.36  
%------------------------------------------------------------------------------