%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 02:28:46 EDT 2022

% Result   : Theorem 0.54s 0.72s
% Output   : Refutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   18 (  18 unt;   0 nHn;  18 RR)
%            Number of literals    :   18 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiplication(skc2,skc3),zero),
    file('KLE148+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(addition(u,zero),u),
    file('KLE148+1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiplication(u,one),u),
    file('KLE148+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(multiplication(zero,u),zero),
    file('KLE148+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(multiplication(skc2,strong_iteration(skc3)),skc2),
    file('KLE148+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE148+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
    file('KLE148+1.p',unknown),
    [] ).

cnf(16,axiom,
    equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
    file('KLE148+1.p',unknown),
    [] ).

cnf(17,axiom,
    equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
    file('KLE148+1.p',unknown),
    [] ).

cnf(22,plain,
    equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
    inference(rew,[status(thm),theory(equality)],[8,11]),
    [iquote('0:Rew:8.0,11.0')] ).

cnf(32,plain,
    equal(addition(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[8,2]),
    [iquote('0:SpR:8.0,2.0')] ).

cnf(105,plain,
    equal(multiplication(skc2,multiplication(skc3,u)),multiplication(zero,u)),
    inference(spr,[status(thm),theory(equality)],[1,16]),
    [iquote('0:SpR:1.0,16.0')] ).

cnf(110,plain,
    equal(multiplication(skc2,multiplication(skc3,u)),zero),
    inference(rew,[status(thm),theory(equality)],[6,105]),
    [iquote('0:Rew:6.0,105.0')] ).

cnf(273,plain,
    equal(addition(multiplication(u,one),multiplication(u,multiplication(v,strong_iteration(v)))),multiplication(u,strong_iteration(v))),
    inference(spr,[status(thm),theory(equality)],[22,17]),
    [iquote('0:SpR:22.0,17.0')] ).

cnf(284,plain,
    equal(addition(u,multiplication(u,multiplication(v,strong_iteration(v)))),multiplication(u,strong_iteration(v))),
    inference(rew,[status(thm),theory(equality)],[4,273]),
    [iquote('0:Rew:4.0,273.0')] ).

cnf(2513,plain,
    equal(multiplication(skc2,strong_iteration(skc3)),addition(skc2,zero)),
    inference(spr,[status(thm),theory(equality)],[110,284]),
    [iquote('0:SpR:110.0,284.0')] ).

cnf(2524,plain,
    equal(multiplication(skc2,strong_iteration(skc3)),skc2),
    inference(rew,[status(thm),theory(equality)],[32,2513,8]),
    [iquote('0:Rew:32.0,2513.0,8.0,2513.0')] ).

cnf(2525,plain,
    $false,
    inference(mrr,[status(thm)],[2524,7]),
    [iquote('0:MRR:2524.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n027.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Thu Jun 16 16:38:35 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.54/0.72  
% 0.54/0.72  SPASS V 3.9 
% 0.54/0.72  SPASS beiseite: Proof found.
% 0.54/0.72  % SZS status Theorem
% 0.54/0.72  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.54/0.72  SPASS derived 1910 clauses, backtracked 0 clauses, performed 0 splits and kept 605 clauses.
% 0.54/0.72  SPASS allocated 87297 KBytes.
% 0.54/0.72  SPASS spent	0:00:00.34 on the problem.
% 0.54/0.72  		0:00:00.03 for the input.
% 0.54/0.72  		0:00:00.03 for the FLOTTER CNF translation.
% 0.54/0.72  		0:00:00.02 for inferences.
% 0.54/0.72  		0:00:00.00 for the backtracking.
% 0.54/0.72  		0:00:00.23 for the reduction.
% 0.54/0.72  
% 0.54/0.72  
% 0.54/0.72  Here is a proof with depth 2, length 18 :
% 0.54/0.72  % SZS output start Refutation
% See solution above
% 0.54/0.72  Formulae used in the proof : goals additive_identity multiplicative_right_identity left_annihilation additive_commutativity infty_unfold1 multiplicative_associativity distributivity1
% 0.54/0.72  
%------------------------------------------------------------------------------