%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 6.13s 6.37s
% Output   : Refutation 6.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   6 unt;   0 nHn;  13 RR)
%            Number of literals    :   28 (   0 equ;  16 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ sum__dfg(u,v,w)
    | ~ sum__dfg(x,v,w)
    | equal(x,u) ),
    file('RNG001-4.p',unknown),
    [] ).

cnf(3,axiom,
    ~ product(a,additive_identity,additive_identity),
    file('RNG001-4.p',unknown),
    [] ).

cnf(4,axiom,
    sum__dfg(additive_identity,u,u),
    file('RNG001-4.p',unknown),
    [] ).

cnf(6,axiom,
    product(u,v,multiply(u,v)),
    file('RNG001-4.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ product(u,v,w)
    | ~ sum__dfg(x,y,v)
    | ~ product(u,y,z)
    | ~ product(u,x,x1)
    | sum__dfg(x1,z,w) ),
    file('RNG001-4.p',unknown),
    [] ).

cnf(52,plain,
    ( ~ sum__dfg(u,v,v)
    | equal(u,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[4,2]),
    [iquote('0:Res:4.0,2.0')] ).

cnf(332,plain,
    ( ~ sum__dfg(u,v,w)
    | ~ product(x,v,y)
    | ~ product(x,u,z)
    | sum__dfg(z,y,multiply(x,w)) ),
    inference(res,[status(thm),theory(equality)],[6,15]),
    [iquote('0:Res:6.0,15.0')] ).

cnf(5288,plain,
    ( ~ product(u,v,w)
    | ~ product(u,additive_identity,x)
    | sum__dfg(x,w,multiply(u,v)) ),
    inference(res,[status(thm),theory(equality)],[4,332]),
    [iquote('0:Res:4.0,332.0')] ).

cnf(18877,plain,
    ( ~ product(u,v,multiply(u,v))
    | ~ product(u,additive_identity,w)
    | equal(w,additive_identity) ),
    inference(res,[status(thm),theory(equality)],[5288,52]),
    [iquote('0:Res:5288.2,52.0')] ).

cnf(18946,plain,
    ( ~ product(u,additive_identity,v)
    | equal(v,additive_identity) ),
    inference(mrr,[status(thm)],[18877,6]),
    [iquote('0:MRR:18877.0,6.0')] ).

cnf(18985,plain,
    equal(multiply(u,additive_identity),additive_identity),
    inference(res,[status(thm),theory(equality)],[6,18946]),
    [iquote('0:Res:6.0,18946.0')] ).

cnf(19028,plain,
    product(u,additive_identity,additive_identity),
    inference(spr,[status(thm),theory(equality)],[18985,6]),
    [iquote('0:SpR:18985.0,6.0')] ).

cnf(19038,plain,
    $false,
    inference(unc,[status(thm)],[19028,3]),
    [iquote('0:UnC:19028.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon May 30 19:15:36 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 6.13/6.37  
% 6.13/6.37  SPASS V 3.9 
% 6.13/6.37  SPASS beiseite: Proof found.
% 6.13/6.37  % SZS status Theorem
% 6.13/6.37  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 6.13/6.37  SPASS derived 14356 clauses, backtracked 0 clauses, performed 0 splits and kept 4133 clauses.
% 6.13/6.37  SPASS allocated 73555 KBytes.
% 6.13/6.37  SPASS spent	0:00:05.95 on the problem.
% 6.13/6.37  		0:00:00.03 for the input.
% 6.13/6.37  		0:00:00.00 for the FLOTTER CNF translation.
% 6.13/6.37  		0:00:00.11 for inferences.
% 6.13/6.37  		0:00:00.00 for the backtracking.
% 6.13/6.37  		0:00:05.76 for the reduction.
% 6.13/6.37  
% 6.13/6.37  
% 6.13/6.37  Here is a proof with depth 5, length 13 :
% 6.13/6.37  % SZS output start Refutation
% See solution above
% 6.13/6.37  Formulae used in the proof : cancellation2 prove_a_times_additive_id_is_additive_id additive_identity1 closure_of_multiplication distributivity1
% 6.13/6.37  
%------------------------------------------------------------------------------