%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 02:28:25 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% 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    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(addition(u,zero),u),
    file('KLE083+1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiplication(one,u),u),
    file('KLE083+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(multiplication(antidomain(u),u),zero),
    file('KLE083+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(antidomain(antidomain(u)),domain__dfg(u)),
    file('KLE083+1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ equal(multiplication(domain__dfg(skc1),skc1),skc1),
    file('KLE083+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE083+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
    file('KLE083+1.p',unknown),
    [] ).

cnf(20,axiom,
    equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
    file('KLE083+1.p',unknown),
    [] ).

cnf(24,plain,
    equal(addition(domain__dfg(u),antidomain(u)),one),
    inference(rew,[status(thm),theory(equality)],[8,13]),
    [iquote('0:Rew:8.0,13.0')] ).

cnf(79,plain,
    equal(addition(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[12,1]),
    [iquote('0:SpR:12.0,1.0')] ).

cnf(360,plain,
    equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),multiplication(one,v)),
    inference(spr,[status(thm),theory(equality)],[24,20]),
    [iquote('0:SpR:24.0,20.0')] ).

cnf(373,plain,
    equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),v),
    inference(rew,[status(thm),theory(equality)],[4,360]),
    [iquote('0:Rew:4.0,360.0')] ).

cnf(1808,plain,
    equal(addition(multiplication(domain__dfg(u),u),zero),u),
    inference(spr,[status(thm),theory(equality)],[7,373]),
    [iquote('0:SpR:7.0,373.0')] ).

cnf(1835,plain,
    equal(multiplication(domain__dfg(u),u),u),
    inference(rew,[status(thm),theory(equality)],[79,1808,12]),
    [iquote('0:Rew:79.0,1808.0,12.0,1808.0')] ).

cnf(1836,plain,
    $false,
    inference(unc,[status(thm)],[1835,11]),
    [iquote('0:UnC:1835.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n007.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 15:19:41 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.54  
% 0.20/0.54  SPASS V 3.9 
% 0.20/0.54  SPASS beiseite: Proof found.
% 0.20/0.54  % SZS status Theorem
% 0.20/0.54  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.54  SPASS derived 1394 clauses, backtracked 0 clauses, performed 0 splits and kept 363 clauses.
% 0.20/0.54  SPASS allocated 86679 KBytes.
% 0.20/0.54  SPASS spent	0:00:00.18 on the problem.
% 0.20/0.54  		0:00:00.04 for the input.
% 0.20/0.54  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.54  		0:00:00.01 for inferences.
% 0.20/0.54  		0:00:00.00 for the backtracking.
% 0.20/0.54  		0:00:00.08 for the reduction.
% 0.20/0.54  
% 0.20/0.54  
% 0.20/0.54  Here is a proof with depth 2, length 15 :
% 0.20/0.54  % SZS output start Refutation
% See solution above
% 0.20/0.54  Formulae used in the proof : additive_identity multiplicative_left_identity domain1 domain4 goals additive_commutativity domain3 left_distributivity
% 0.20/0.54  
%------------------------------------------------------------------------------