%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG038-2 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:41:17 EDT 2022

% Result   : Unsatisfiable 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   19 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(10,axiom,
    sum__dfg(u,additive_identity,u),
    file('RNG038-2.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(u,v,x)
    | equalish(x,w) ),
    file('RNG038-2.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equalish(x,w) ),
    file('RNG038-2.p',unknown),
    [] ).

cnf(25,axiom,
    product(additive_identity,u,additive_identity),
    file('RNG038-2.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ equalish(u,additive_identity)
    | product(u,h(u,v),v) ),
    file('RNG038-2.p',unknown),
    [] ).

cnf(29,axiom,
    ~ equalish(a,additive_identity),
    file('RNG038-2.p',unknown),
    [] ).

cnf(34,plain,
    ( ~ product(u,v,additive_identity)
    | ~ product(u,v,a) ),
    inference(res,[status(thm),theory(equality)],[24,29]),
    [iquote('0:Res:24.2,29.0')] ).

cnf(50,plain,
    ~ product(additive_identity,u,a),
    inference(res,[status(thm),theory(equality)],[25,34]),
    [iquote('0:Res:25.0,34.0')] ).

cnf(53,plain,
    ~ equalish(additive_identity,additive_identity),
    inference(res,[status(thm),theory(equality)],[27,50]),
    [iquote('0:Res:27.1,50.0')] ).

cnf(182,plain,
    ( ~ sum__dfg(u,additive_identity,v)
    | equalish(v,u) ),
    inference(res,[status(thm),theory(equality)],[10,23]),
    [iquote('0:Res:10.0,23.0')] ).

cnf(194,plain,
    equalish(u,u),
    inference(res,[status(thm),theory(equality)],[10,182]),
    [iquote('0:Res:10.0,182.0')] ).

cnf(205,plain,
    $false,
    inference(unc,[status(thm)],[194,53]),
    [iquote('0:UnC:194.0,53.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : RNG038-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n020.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 May 30 19:33:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.42  
% 0.18/0.42  SPASS V 3.9 
% 0.18/0.42  SPASS beiseite: Proof found.
% 0.18/0.42  % SZS status Theorem
% 0.18/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.42  SPASS derived 174 clauses, backtracked 0 clauses, performed 0 splits and kept 143 clauses.
% 0.18/0.42  SPASS allocated 63248 KBytes.
% 0.18/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.18/0.42  		0:00:00.03 for the input.
% 0.18/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42  		0:00:00.00 for inferences.
% 0.18/0.42  		0:00:00.00 for the backtracking.
% 0.18/0.42  		0:00:00.01 for the reduction.
% 0.18/0.42  
% 0.18/0.42  
% 0.18/0.42  Here is a proof with depth 3, length 12 :
% 0.18/0.42  % SZS output start Refutation
% See solution above
% 0.18/0.42  Formulae used in the proof : additive_identity2 addition_is_well_defined multiplication_is_well_defined multiplicative_identity1 some_property a_not_additive_identity
% 0.18/0.42  
%------------------------------------------------------------------------------