%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE070+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 02:28:22 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   9 RR)
%            Number of literals    :    9 (   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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    equal(multiplication(u,one),u),
    file('KLE070+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(addition(domain__dfg(u),one),one),
    file('KLE070+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE070+1.p',unknown),
    [] ).

cnf(17,axiom,
    ~ equal(addition(domain__dfg(skc3),multiplication(domain__dfg(skc3),domain__dfg(skc2))),domain__dfg(skc3)),
    file('KLE070+1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
    file('KLE070+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(826,plain,
    equal(addition(multiplication(u,one),multiplication(u,domain__dfg(v))),multiplication(u,one)),
    inference(spr,[status(thm),theory(equality)],[20,18]),
    [iquote('0:SpR:20.0,18.0')] ).

cnf(836,plain,
    equal(addition(u,multiplication(u,domain__dfg(v))),u),
    inference(rew,[status(thm),theory(equality)],[4,826]),
    [iquote('0:Rew:4.0,826.0')] ).

cnf(837,plain,
    $false,
    inference(unc,[status(thm)],[836,17]),
    [iquote('0:UnC:836.0,17.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : KLE070+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n008.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 12:09:37 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.49  
% 0.20/0.49  SPASS V 3.9 
% 0.20/0.49  SPASS beiseite: Proof found.
% 0.20/0.49  % SZS status Theorem
% 0.20/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.49  SPASS derived 583 clauses, backtracked 0 clauses, performed 0 splits and kept 140 clauses.
% 0.20/0.49  SPASS allocated 85783 KBytes.
% 0.20/0.49  SPASS spent	0:00:00.13 on the problem.
% 0.20/0.49  		0:00:00.04 for the input.
% 0.20/0.49  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.49  		0:00:00.01 for inferences.
% 0.20/0.49  		0:00:00.00 for the backtracking.
% 0.20/0.49  		0:00:00.03 for the reduction.
% 0.20/0.49  
% 0.20/0.49  
% 0.20/0.49  Here is a proof with depth 1, length 9 :
% 0.20/0.49  % SZS output start Refutation
% See solution above
% 0.20/0.49  Formulae used in the proof : multiplicative_right_identity domain3 additive_commutativity goals right_distributivity
% 0.20/0.49  
%------------------------------------------------------------------------------