%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE067+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   9 RR)
%            Number of literals    :    9 (   0 equ;   2 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('KLE067+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE067+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
    file('KLE067+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
    file('KLE067+1.p',unknown),
    [] ).

cnf(17,axiom,
    ~ equal(domain__dfg(addition(domain__dfg(skc3),domain__dfg(skc2))),addition(domain__dfg(skc3),domain__dfg(skc2))),
    file('KLE067+1.p',unknown),
    [] ).

cnf(21,plain,
    ~ equal(domain__dfg(domain__dfg(addition(skc2,skc3))),domain__dfg(addition(skc2,skc3))),
    inference(rew,[status(thm),theory(equality)],[9,17,13]),
    [iquote('0:Rew:9.0,17.0,13.0,17.0')] ).

cnf(91,plain,
    equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
    inference(spr,[status(thm),theory(equality)],[5,12]),
    [iquote('0:SpR:5.0,12.0')] ).

cnf(94,plain,
    equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[5,91]),
    [iquote('0:Rew:5.0,91.0')] ).

cnf(95,plain,
    $false,
    inference(unc,[status(thm)],[94,21]),
    [iquote('0:UnC:94.0,21.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KLE067+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 15:06:11 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  
% 0.19/0.45  SPASS V 3.9 
% 0.19/0.45  SPASS beiseite: Proof found.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 64 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.19/0.45  SPASS allocated 85153 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.45  		0:00:00.04 for the input.
% 0.19/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45  		0:00:00.00 for inferences.
% 0.19/0.45  		0:00:00.00 for the backtracking.
% 0.19/0.45  		0:00:00.00 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 1, length 9 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : multiplicative_left_identity additive_commutativity domain2 domain5 goals
% 0.19/0.45  
%------------------------------------------------------------------------------