%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP017-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 11:44:47 EDT 2022

% Result   : Unsatisfiable 0.19s 0.46s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (   7 unt;   0 nHn;  15 RR)
%            Number of literals    :   28 (   0 equ;  17 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;  10 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    product(b,a,identity),
    file('GRP017-1.p',unknown),
    [] ).

cnf(3,axiom,
    product(a,c,identity),
    file('GRP017-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(c,b),
    file('GRP017-1.p',unknown),
    [] ).

cnf(6,axiom,
    product(identity,u,u),
    file('GRP017-1.p',unknown),
    [] ).

cnf(7,axiom,
    product(u,identity,u),
    file('GRP017-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equal(x,w) ),
    file('GRP017-1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,v,y)
    | ~ product(z,x,u)
    | product(z,y,w) ),
    file('GRP017-1.p',unknown),
    [] ).

cnf(14,plain,
    ( ~ product(u,v,b)
    | ~ product(u,v,c) ),
    inference(res,[status(thm),theory(equality)],[11,5]),
    [iquote('0:Res:11.2,5.0')] ).

cnf(45,plain,
    ( ~ product(u,a,v)
    | ~ product(w,u,b)
    | product(w,v,identity) ),
    inference(res,[status(thm),theory(equality)],[2,12]),
    [iquote('0:Res:2.0,12.0')] ).

cnf(50,plain,
    ( ~ product(u,v,w)
    | ~ product(x,u,identity)
    | product(x,w,v) ),
    inference(res,[status(thm),theory(equality)],[6,12]),
    [iquote('0:Res:6.0,12.0')] ).

cnf(155,plain,
    ( ~ product(u,identity,b)
    | product(u,a,identity) ),
    inference(res,[status(thm),theory(equality)],[6,45]),
    [iquote('0:Res:6.0,45.0')] ).

cnf(292,plain,
    ( ~ product(u,a,identity)
    | product(u,identity,c) ),
    inference(res,[status(thm),theory(equality)],[3,50]),
    [iquote('0:Res:3.0,50.0')] ).

cnf(537,plain,
    ( ~ product(u,a,identity)
    | ~ product(u,identity,b) ),
    inference(res,[status(thm),theory(equality)],[292,14]),
    [iquote('0:Res:292.1,14.1')] ).

cnf(552,plain,
    ~ product(u,identity,b),
    inference(mrr,[status(thm)],[537,155]),
    [iquote('0:MRR:537.0,155.1')] ).

cnf(553,plain,
    $false,
    inference(unc,[status(thm)],[552,7]),
    [iquote('0:UnC:552.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GRP017-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.11  % Command  : run_spass %d %s
% 0.12/0.32  % Computer : n026.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Mon Jun 13 12:51:36 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.19/0.46  
% 0.19/0.46  SPASS V 3.9 
% 0.19/0.46  SPASS beiseite: Proof found.
% 0.19/0.46  % SZS status Theorem
% 0.19/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.46  SPASS derived 451 clauses, backtracked 0 clauses, performed 0 splits and kept 264 clauses.
% 0.19/0.46  SPASS allocated 63437 KBytes.
% 0.19/0.46  SPASS spent	0:00:00.12 on the problem.
% 0.19/0.46  		0:00:00.03 for the input.
% 0.19/0.46  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46  		0:00:00.01 for inferences.
% 0.19/0.46  		0:00:00.00 for the backtracking.
% 0.19/0.46  		0:00:00.06 for the reduction.
% 0.19/0.46  
% 0.19/0.46  
% 0.19/0.46  Here is a proof with depth 3, length 15 :
% 0.19/0.46  % SZS output start Refutation
% See solution above
% 0.19/0.46  Formulae used in the proof : b_times_a_is_identity a_times_c_is_identity prove_b_equals_c left_identity right_identity total_function2 associativity1
% 0.19/0.46  
%------------------------------------------------------------------------------