%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE061+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 02:28:19 EDT 2022

% Result   : Theorem 0.18s 0.47s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  15 unt;   0 nHn;  15 RR)
%            Number of literals    :   15 (   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(5,axiom,
    equal(multiplication(one,u),u),
    file('KLE061+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(addition(domain__dfg(u),one),one),
    file('KLE061+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE061+1.p',unknown),
    [] ).

cnf(10,axiom,
    ~ equal(multiplication(domain__dfg(skc1),domain__dfg(skc1)),domain__dfg(skc1)),
    file('KLE061+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
    file('KLE061+1.p',unknown),
    [] ).

cnf(17,axiom,
    equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
    file('KLE061+1.p',unknown),
    [] ).

cnf(19,axiom,
    equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
    file('KLE061+1.p',unknown),
    [] ).

cnf(20,plain,
    equal(addition(one,domain__dfg(u)),one),
    inference(rew,[status(thm),theory(equality)],[9,8]),
    [iquote('0:Rew:9.0,8.0')] ).

cnf(166,plain,
    equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
    inference(spr,[status(thm),theory(equality)],[5,13]),
    [iquote('0:SpR:5.0,13.0')] ).

cnf(169,plain,
    equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[5,166]),
    [iquote('0:Rew:5.0,166.0')] ).

cnf(312,plain,
    equal(addition(domain__dfg(u),multiplication(domain__dfg(u),domain__dfg(u))),multiplication(domain__dfg(u),domain__dfg(u))),
    inference(spr,[status(thm),theory(equality)],[169,17]),
    [iquote('0:SpR:169.0,17.0')] ).

cnf(768,plain,
    equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
    inference(spr,[status(thm),theory(equality)],[20,19]),
    [iquote('0:SpR:20.0,19.0')] ).

cnf(778,plain,
    equal(addition(u,multiplication(domain__dfg(v),u)),u),
    inference(rew,[status(thm),theory(equality)],[5,768]),
    [iquote('0:Rew:5.0,768.0')] ).

cnf(781,plain,
    equal(multiplication(domain__dfg(u),domain__dfg(u)),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[778,312]),
    [iquote('0:Rew:778.0,312.0')] ).

cnf(787,plain,
    $false,
    inference(unc,[status(thm)],[781,10]),
    [iquote('0:UnC:781.0,10.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : KLE061+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.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 : Thu Jun 16 12:11:11 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.47  
% 0.18/0.47  SPASS V 3.9 
% 0.18/0.47  SPASS beiseite: Proof found.
% 0.18/0.47  % SZS status Theorem
% 0.18/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.47  SPASS derived 537 clauses, backtracked 0 clauses, performed 0 splits and kept 135 clauses.
% 0.18/0.47  SPASS allocated 85789 KBytes.
% 0.18/0.47  SPASS spent	0:00:00.13 on the problem.
% 0.18/0.47  		0:00:00.03 for the input.
% 0.18/0.47  		0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.47  		0:00:00.01 for inferences.
% 0.18/0.47  		0:00:00.00 for the backtracking.
% 0.18/0.47  		0:00:00.04 for the reduction.
% 0.18/0.47  
% 0.18/0.47  
% 0.18/0.47  Here is a proof with depth 2, length 15 :
% 0.18/0.47  % SZS output start Refutation
% See solution above
% 0.18/0.47  Formulae used in the proof : multiplicative_left_identity domain3 additive_commutativity goals domain2 domain1 left_distributivity
% 0.18/0.47  
%------------------------------------------------------------------------------