%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV880-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 21:45:28 EDT 2022

% Result   : Unsatisfiable 0.41s 0.61s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   9 unt;   0 nHn;  12 RR)
%            Number of literals    :   16 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;  12 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(411,axiom,
    ( ~ c_in(u,v,w)
    | ~ c_lessequals(x,v,tc_fun(w,tc_bool))
    | c_lessequals(c_Set_Oinsert(u,x,w),v,tc_fun(w,tc_bool)) ),
    file('SWV880-1.p',unknown),
    [] ).

cnf(441,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)),
    file('SWV880-1.p',unknown),
    [] ).

cnf(473,axiom,
    ( ~ c_in(u,v,w)
    | c_in(hAPP(x,u),c_Set_Oimage(x,v,w,y),y) ),
    file('SWV880-1.p',unknown),
    [] ).

cnf(505,axiom,
    equal(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G),
    file('SWV880-1.p',unknown),
    [] ).

cnf(506,axiom,
    c_in(v_pn,v_U,tc_Com_Opname),
    file('SWV880-1.p',unknown),
    [] ).

cnf(507,axiom,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    file('SWV880-1.p',unknown),
    [] ).

cnf(508,plain,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool)),
    inference(rew,[status(thm),theory(equality)],[505,507]),
    [iquote('0:Rew:505.0,507.0')] ).

cnf(582,plain,
    c_in(hAPP(u,v_pn),c_Set_Oimage(u,v_U,tc_Com_Opname,v),v),
    inference(res,[status(thm),theory(equality)],[506,473]),
    [iquote('0:Res:506.0,473.0')] ).

cnf(609,plain,
    ( ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_G,tc_fun(t_a,tc_bool))
    | ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a) ),
    inference(res,[status(thm),theory(equality)],[411,508]),
    [iquote('0:Res:411.2,508.0')] ).

cnf(639,plain,
    ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
    inference(mrr,[status(thm)],[609,441]),
    [iquote('0:MRR:609.0,441.0')] ).

cnf(704,plain,
    c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
    inference(spr,[status(thm),theory(equality)],[505,582]),
    [iquote('0:SpR:505.0,582.0')] ).

cnf(708,plain,
    $false,
    inference(mrr,[status(thm)],[704,639]),
    [iquote('0:MRR:704.0,639.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV880-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n022.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 05:46:17 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.41/0.61  
% 0.41/0.61  SPASS V 3.9 
% 0.41/0.61  SPASS beiseite: Proof found.
% 0.41/0.61  % SZS status Theorem
% 0.41/0.61  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.41/0.61  SPASS derived 156 clauses, backtracked 0 clauses, performed 0 splits and kept 513 clauses.
% 0.41/0.61  SPASS allocated 76708 KBytes.
% 0.41/0.61  SPASS spent	0:00:00.25 on the problem.
% 0.41/0.61  		0:00:00.05 for the input.
% 0.41/0.61  		0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.61  		0:00:00.00 for inferences.
% 0.41/0.61  		0:00:00.00 for the backtracking.
% 0.41/0.61  		0:00:00.08 for the reduction.
% 0.41/0.61  
% 0.41/0.61  
% 0.41/0.61  Here is a proof with depth 2, length 12 :
% 0.41/0.61  % SZS output start Refutation
% See solution above
% 0.41/0.61  Formulae used in the proof : cls_insert__subset_2 cls_empty__subsetI_0 cls_imageI_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.41/0.61  
%------------------------------------------------------------------------------