%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV254-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 : Wed Jul 20 21:41:50 EDT 2022

% Result   : Unsatisfiable 1.62s 1.81s
% Output   : Refutation 1.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (  10 unt;   0 nHn;  13 RR)
%            Number of literals    :   16 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(17,axiom,
    c_lessequals(u,v_x(u),tc_nat),
    file('SWV254-1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(v_x(u),v_nat),
    file('SWV254-1.p',unknown),
    [] ).

cnf(1191,axiom,
    ~ equal(c_Datatype_Ooption_OSome(u,v),c_Datatype_Ooption_ONone),
    file('SWV254-1.p',unknown),
    [] ).

cnf(1817,axiom,
    ( ~ c_lessequals(u,v,tc_nat)
    | equal(c_minus(v,c_minus(v,u,tc_nat),tc_nat),u) ),
    file('SWV254-1.p',unknown),
    [] ).

cnf(1818,axiom,
    ( ~ c_lessequals(u,v,tc_nat)
    | equal(c_minus(c_plus(w,u,tc_nat),v,tc_nat),c_minus(w,c_minus(v,u,tc_nat),tc_nat)) ),
    file('SWV254-1.p',unknown),
    [] ).

cnf(2057,axiom,
    ( ~ c_lessequals(u,v,tc_nat)
    | equal(c_minus(u,v,tc_nat),c_0) ),
    file('SWV254-1.p',unknown),
    [] ).

cnf(2794,plain,
    c_lessequals(u,v_nat,tc_nat),
    inference(rew,[status(thm),theory(equality)],[18,17]),
    [iquote('0:Rew:18.0,17.0')] ).

cnf(2982,plain,
    equal(c_minus(c_plus(u,v,tc_nat),v_nat,tc_nat),c_minus(u,c_minus(v_nat,v,tc_nat),tc_nat)),
    inference(res,[status(thm),theory(equality)],[2794,1818]),
    [iquote('0:Res:2794.0,1818.0')] ).

cnf(2991,plain,
    equal(c_minus(v_nat,c_minus(v_nat,u,tc_nat),tc_nat),u),
    inference(res,[status(thm),theory(equality)],[2794,1817]),
    [iquote('0:Res:2794.0,1817.0')] ).

cnf(2994,plain,
    equal(c_minus(u,v_nat,tc_nat),c_0),
    inference(res,[status(thm),theory(equality)],[2794,2057]),
    [iquote('0:Res:2794.0,2057.0')] ).

cnf(3094,plain,
    equal(c_minus(u,c_minus(v_nat,v,tc_nat),tc_nat),c_0),
    inference(rew,[status(thm),theory(equality)],[2994,2982]),
    [iquote('0:Rew:2994.0,2982.0')] ).

cnf(3095,plain,
    equal(c_0,u),
    inference(rew,[status(thm),theory(equality)],[3094,2991]),
    [iquote('0:Rew:3094.0,2991.0')] ).

cnf(3096,plain,
    $false,
    inference(aed,[status(thm),theory(equality)],[1191,3095]),
    [iquote('0:AED:1191.0,3095.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SWV254-1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n028.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 06:53:41 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 1.62/1.81  
% 1.62/1.81  SPASS V 3.9 
% 1.62/1.81  SPASS beiseite: Proof found.
% 1.62/1.81  % SZS status Theorem
% 1.62/1.81  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.62/1.81  SPASS derived 113 clauses, backtracked 0 clauses, performed 0 splits and kept 2692 clauses.
% 1.62/1.81  SPASS allocated 80061 KBytes.
% 1.62/1.81  SPASS spent	0:00:01.38 on the problem.
% 1.62/1.81  		0:00:00.21 for the input.
% 1.62/1.81  		0:00:00.00 for the FLOTTER CNF translation.
% 1.62/1.81  		0:00:00.00 for inferences.
% 1.62/1.81  		0:00:00.00 for the backtracking.
% 1.62/1.81  		0:00:00.79 for the reduction.
% 1.62/1.81  
% 1.62/1.81  
% 1.62/1.81  Here is a proof with depth 1, length 13 :
% 1.62/1.81  % SZS output start Refutation
% See solution above
% 1.62/1.81  Formulae used in the proof : cls_conjecture_0 cls_conjecture_1 cls_Datatype_Ooption_Odistinct__1_0 cls_NatArith_Odiff__diff__cancel_0 cls_NatArith_Odiff__diff__right_0 cls_Nat_Odiff__is__0__eq_H_0
% 1.62/1.81  
%------------------------------------------------------------------------------