%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 20:41:10 EDT 2022

% Result   : Unsatisfiable 0.18s 0.43s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   7 unt;   0 nHn;  14 RR)
%            Number of literals    :   25 (   0 equ;  15 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,
    sum__dfg(a,b,d),
    file('RNG002-1.p',unknown),
    [] ).

cnf(2,axiom,
    sum__dfg(a,c,d),
    file('RNG002-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(c,b),
    file('RNG002-1.p',unknown),
    [] ).

cnf(4,axiom,
    sum__dfg(additive_identity,u,u),
    file('RNG002-1.p',unknown),
    [] ).

cnf(8,axiom,
    sum__dfg(additive_inverse(u),u,additive_identity),
    file('RNG002-1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,v,y)
    | ~ sum__dfg(z,x,u)
    | sum__dfg(z,y,w) ),
    file('RNG002-1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(u,v,x)
    | equal(x,w) ),
    file('RNG002-1.p',unknown),
    [] ).

cnf(21,plain,
    ( ~ sum__dfg(u,v,b)
    | ~ sum__dfg(u,v,c) ),
    inference(res,[status(thm),theory(equality)],[19,3]),
    [iquote('0:Res:19.2,3.0')] ).

cnf(124,plain,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,u,additive_identity)
    | sum__dfg(x,w,v) ),
    inference(res,[status(thm),theory(equality)],[4,10]),
    [iquote('0:Res:4.0,10.0')] ).

cnf(326,plain,
    ( ~ sum__dfg(u,a,additive_identity)
    | sum__dfg(u,d,c) ),
    inference(res,[status(thm),theory(equality)],[2,124]),
    [iquote('0:Res:2.0,124.0')] ).

cnf(327,plain,
    ( ~ sum__dfg(u,a,additive_identity)
    | sum__dfg(u,d,b) ),
    inference(res,[status(thm),theory(equality)],[1,124]),
    [iquote('0:Res:1.0,124.0')] ).

cnf(348,plain,
    ( ~ sum__dfg(u,a,additive_identity)
    | ~ sum__dfg(u,d,b) ),
    inference(res,[status(thm),theory(equality)],[326,21]),
    [iquote('0:Res:326.1,21.1')] ).

cnf(353,plain,
    ~ sum__dfg(u,a,additive_identity),
    inference(mrr,[status(thm)],[348,327]),
    [iquote('0:MRR:348.1,327.1')] ).

cnf(354,plain,
    $false,
    inference(unc,[status(thm)],[353,8]),
    [iquote('0:UnC:353.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : RNG002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n029.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 14:00:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.43  
% 0.18/0.43  SPASS V 3.9 
% 0.18/0.43  SPASS beiseite: Proof found.
% 0.18/0.43  % SZS status Theorem
% 0.18/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.43  SPASS derived 296 clauses, backtracked 0 clauses, performed 0 splits and kept 156 clauses.
% 0.18/0.43  SPASS allocated 63318 KBytes.
% 0.18/0.43  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.43  		0:00:00.03 for the input.
% 0.18/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43  		0:00:00.00 for inferences.
% 0.18/0.43  		0:00:00.00 for the backtracking.
% 0.18/0.43  		0:00:00.03 for the reduction.
% 0.18/0.43  
% 0.18/0.43  
% 0.18/0.43  Here is a proof with depth 3, length 14 :
% 0.18/0.43  % SZS output start Refutation
% See solution above
% 0.18/0.43  Formulae used in the proof : a_plus_b_is_d a_plus_c_is_d prove_b_equals_c additive_identity1 left_inverse associativity_of_addition1 addition_is_well_defined
% 0.18/0.43  
%------------------------------------------------------------------------------