%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE065+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 02:28:20 EDT 2022

% Result   : Theorem 0.61s 0.86s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% 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(domain__dfg(zero),zero),
    file('KLE065+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(multiplication(skc2,skc3),zero),
    file('KLE065+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(multiplication(one,u),u),
    file('KLE065+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(multiplication(zero,u),zero),
    file('KLE065+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(addition(domain__dfg(u),one),one),
    file('KLE065+1.p',unknown),
    [] ).

cnf(10,axiom,
    ~ equal(multiplication(skc2,domain__dfg(skc3)),zero),
    file('KLE065+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE065+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
    file('KLE065+1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
    file('KLE065+1.p',unknown),
    [] ).

cnf(20,axiom,
    equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
    file('KLE065+1.p',unknown),
    [] ).

cnf(21,plain,
    equal(addition(one,domain__dfg(u)),one),
    inference(rew,[status(thm),theory(equality)],[11,9]),
    [iquote('0:Rew:11.0,9.0')] ).

cnf(261,plain,
    equal(addition(multiplication(u,domain__dfg(v)),multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v)))),multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v)))),
    inference(spr,[status(thm),theory(equality)],[14,18]),
    [iquote('0:SpR:14.0,18.0')] ).

cnf(690,plain,
    equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
    inference(spr,[status(thm),theory(equality)],[21,20]),
    [iquote('0:SpR:21.0,20.0')] ).

cnf(700,plain,
    equal(addition(u,multiplication(domain__dfg(v),u)),u),
    inference(rew,[status(thm),theory(equality)],[6,690]),
    [iquote('0:Rew:6.0,690.0')] ).

cnf(702,plain,
    equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
    inference(rew,[status(thm),theory(equality)],[700,261]),
    [iquote('0:Rew:700.0,261.0')] ).

cnf(4987,plain,
    equal(multiplication(domain__dfg(zero),multiplication(skc2,domain__dfg(skc3))),multiplication(skc2,domain__dfg(skc3))),
    inference(spr,[status(thm),theory(equality)],[2,702]),
    [iquote('0:SpR:2.0,702.0')] ).

cnf(5009,plain,
    equal(multiplication(skc2,domain__dfg(skc3)),zero),
    inference(rew,[status(thm),theory(equality)],[8,4987,1]),
    [iquote('0:Rew:8.0,4987.0,1.0,4987.0')] ).

cnf(5010,plain,
    $false,
    inference(mrr,[status(thm)],[5009,10]),
    [iquote('0:MRR:5009.0,10.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KLE065+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n023.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 08:01:05 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.61/0.86  
% 0.61/0.86  SPASS V 3.9 
% 0.61/0.86  SPASS beiseite: Proof found.
% 0.61/0.86  % SZS status Theorem
% 0.61/0.86  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.61/0.86  SPASS derived 3698 clauses, backtracked 0 clauses, performed 0 splits and kept 695 clauses.
% 0.61/0.86  SPASS allocated 88968 KBytes.
% 0.61/0.86  SPASS spent	0:00:00.49 on the problem.
% 0.61/0.86  		0:00:00.04 for the input.
% 0.61/0.86  		0:00:00.03 for the FLOTTER CNF translation.
% 0.61/0.86  		0:00:00.03 for inferences.
% 0.61/0.86  		0:00:00.00 for the backtracking.
% 0.61/0.86  		0:00:00.37 for the reduction.
% 0.61/0.86  
% 0.61/0.86  
% 0.61/0.86  Here is a proof with depth 2, length 18 :
% 0.61/0.86  % SZS output start Refutation
% See solution above
% 0.61/0.86  Formulae used in the proof : domain4 goals multiplicative_left_identity left_annihilation domain3 additive_commutativity domain2 domain1 left_distributivity
% 0.61/0.86  
%------------------------------------------------------------------------------