%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 : Sun Jul 17 02:28:21 EDT 2022

% Result   : Theorem 0.21s 0.46s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;  14 RR)
%            Number of literals    :   14 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(domain__dfg(zero),zero),
    file('KLE066+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(addition(u,zero),u),
    file('KLE066+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(multiplication(zero,u),zero),
    file('KLE066+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(multiplication(skc2,domain__dfg(skc3)),zero),
    file('KLE066+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(multiplication(skc2,skc3),zero),
    file('KLE066+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE066+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
    file('KLE066+1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
    file('KLE066+1.p',unknown),
    [] ).

cnf(37,plain,
    equal(addition(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[11,2]),
    [iquote('0:SpR:11.0,2.0')] ).

cnf(157,plain,
    equal(domain__dfg(multiplication(skc2,skc3)),domain__dfg(zero)),
    inference(spr,[status(thm),theory(equality)],[8,14]),
    [iquote('0:SpR:8.0,14.0')] ).

cnf(160,plain,
    equal(domain__dfg(multiplication(skc2,skc3)),zero),
    inference(rew,[status(thm),theory(equality)],[1,157]),
    [iquote('0:Rew:1.0,157.0')] ).

cnf(253,plain,
    equal(addition(multiplication(skc2,skc3),multiplication(zero,multiplication(skc2,skc3))),multiplication(zero,multiplication(skc2,skc3))),
    inference(spr,[status(thm),theory(equality)],[160,18]),
    [iquote('0:SpR:160.0,18.0')] ).

cnf(259,plain,
    equal(multiplication(skc2,skc3),zero),
    inference(rew,[status(thm),theory(equality)],[37,253,11,7]),
    [iquote('0:Rew:37.0,253.0,11.0,253.0,7.0,253.0')] ).

cnf(260,plain,
    $false,
    inference(mrr,[status(thm)],[259,9]),
    [iquote('0:MRR:259.0,9.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Thu Jun 16 15:34:20 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.46  
% 0.21/0.46  SPASS V 3.9 
% 0.21/0.46  SPASS beiseite: Proof found.
% 0.21/0.46  % SZS status Theorem
% 0.21/0.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.46  SPASS derived 178 clauses, backtracked 0 clauses, performed 0 splits and kept 66 clauses.
% 0.21/0.46  SPASS allocated 85303 KBytes.
% 0.21/0.46  SPASS spent	0:00:00.09 on the problem.
% 0.21/0.46  		0:00:00.04 for the input.
% 0.21/0.46  		0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.46  		0:00:00.00 for inferences.
% 0.21/0.46  		0:00:00.00 for the backtracking.
% 0.21/0.46  		0:00:00.01 for the reduction.
% 0.21/0.46  
% 0.21/0.46  
% 0.21/0.46  Here is a proof with depth 2, length 14 :
% 0.21/0.46  % SZS output start Refutation
% See solution above
% 0.21/0.46  Formulae used in the proof : domain4 additive_identity left_annihilation goals additive_commutativity domain2 domain1
% 0.21/0.46  
%------------------------------------------------------------------------------