%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV678-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 21:44:47 EDT 2022

% Result   : Unsatisfiable 0.41s 0.57s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   5 unt;   1 nHn;   9 RR)
%            Number of literals    :   16 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(603,axiom,
    ( ~ class_Ring__and__Field_Ofield(u)
    | ~ c_lessequals(v,w,tc_nat)
    | equal(x,c_HOL_Ozero__class_Ozero(u))
    | equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(x,w,u),c_Power_Opower__class_Opower(x,v,u),u),c_Power_Opower__class_Opower(x,c_HOL_Ominus__class_Ominus(w,v,tc_nat),u)) ),
    file('SWV678-1.p',unknown),
    [] ).

cnf(639,axiom,
    c_lessequals(v_n,v_m,tc_nat),
    file('SWV678-1.p',unknown),
    [] ).

cnf(640,axiom,
    ( ~ class_Ring__and__Field_Ofield(t_a)
    | ~ equal(c_HOL_Ozero__class_Ozero(t_a),v_a) ),
    file('SWV678-1.p',unknown),
    [] ).

cnf(684,axiom,
    class_Ring__and__Field_Ofield(t_a),
    file('SWV678-1.p',unknown),
    [] ).

cnf(686,axiom,
    ( ~ equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a))
    | ~ c_lessequals(v_n,v_m,tc_nat) ),
    file('SWV678-1.p',unknown),
    [] ).

cnf(688,plain,
    ~ equal(c_HOL_Ozero__class_Ozero(t_a),v_a),
    inference(mrr,[status(thm)],[640,684]),
    [iquote('0:MRR:640.0,684.0')] ).

cnf(709,plain,
    ~ equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a)),
    inference(mrr,[status(thm)],[686,639]),
    [iquote('0:MRR:686.1,639.0')] ).

cnf(858,plain,
    ( ~ class_Ring__and__Field_Ofield(t_a)
    | ~ c_lessequals(v_n,v_m,tc_nat)
    | equal(c_HOL_Ozero__class_Ozero(t_a),v_a) ),
    inference(res,[status(thm),theory(equality)],[603,709]),
    [iquote('0:Res:603.2,709.0')] ).

cnf(894,plain,
    $false,
    inference(mrr,[status(thm)],[858,684,639,688]),
    [iquote('0:MRR:858.0,858.1,858.2,684.0,639.0,688.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV678-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n010.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Wed Jun 15 17:16:24 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.41/0.57  
% 0.41/0.57  SPASS V 3.9 
% 0.41/0.57  SPASS beiseite: Proof found.
% 0.41/0.57  % SZS status Theorem
% 0.41/0.57  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.41/0.57  SPASS derived 99 clauses, backtracked 0 clauses, performed 0 splits and kept 575 clauses.
% 0.41/0.57  SPASS allocated 76690 KBytes.
% 0.41/0.57  SPASS spent	0:00:00.21 on the problem.
% 0.41/0.57  		0:00:00.06 for the input.
% 0.41/0.57  		0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.57  		0:00:00.00 for inferences.
% 0.41/0.57  		0:00:00.00 for the backtracking.
% 0.41/0.57  		0:00:00.08 for the reduction.
% 0.41/0.57  
% 0.41/0.57  
% 0.41/0.57  Here is a proof with depth 1, length 9 :
% 0.41/0.57  % SZS output start Refutation
% See solution above
% 0.41/0.57  Formulae used in the proof : cls_power__diff_0 cls_CHAINED_0 cls_CHAINED_0_01 tfree_tcs cls_conjecture_1
% 0.41/0.57  
%------------------------------------------------------------------------------