%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV258-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 21:41:52 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   10 (   6 unt;   0 nHn;  10 RR)
%            Number of literals    :   15 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_lessequals(c_Message_Oparts(u),c_Message_Oparts(v),tc_set(tc_Message_Omsg))
    | c_lessequals(u,c_Message_Oparts(v),tc_set(tc_Message_Omsg)) ),
    file('SWV258-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ c_lessequals(u,c_Message_Oparts(v),tc_set(tc_Message_Omsg))
    | c_lessequals(c_Message_Oparts(u),c_Message_Oparts(v),tc_set(tc_Message_Omsg)) ),
    file('SWV258-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ c_in(u,v,w)
    | ~ c_lessequals(x,v,tc_set(w))
    | c_lessequals(c_insert(u,x,w),v,tc_set(w)) ),
    file('SWV258-2.p',unknown),
    [] ).

cnf(4,axiom,
    c_lessequals(u,u,tc_set(v)),
    file('SWV258-2.p',unknown),
    [] ).

cnf(5,axiom,
    c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
    file('SWV258-2.p',unknown),
    [] ).

cnf(6,axiom,
    ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
    file('SWV258-2.p',unknown),
    [] ).

cnf(9,plain,
    ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
    inference(res,[status(thm),theory(equality)],[2,6]),
    [iquote('0:Res:2.1,6.0')] ).

cnf(11,plain,
    c_lessequals(u,c_Message_Oparts(u),tc_set(tc_Message_Omsg)),
    inference(res,[status(thm),theory(equality)],[4,1]),
    [iquote('0:Res:4.0,1.0')] ).

cnf(16,plain,
    ( ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
    | ~ c_lessequals(v_H,c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
    inference(res,[status(thm),theory(equality)],[3,9]),
    [iquote('0:Res:3.2,9.0')] ).

cnf(17,plain,
    $false,
    inference(mrr,[status(thm)],[16,5,11]),
    [iquote('0:MRR:16.0,16.1,5.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SWV258-2 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.10  % Command  : run_spass %d %s
% 0.10/0.28  % Computer : n007.cluster.edu
% 0.10/0.28  % Model    : x86_64 x86_64
% 0.10/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28  % Memory   : 8042.1875MB
% 0.10/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28  % CPULimit : 300
% 0.10/0.28  % WCLimit  : 600
% 0.10/0.28  % DateTime : Tue Jun 14 17:10:39 EDT 2022
% 0.10/0.28  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35  SPASS V 3.9 
% 0.13/0.35  SPASS beiseite: Proof found.
% 0.13/0.35  % SZS status Theorem
% 0.13/0.35  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.13/0.35  SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.13/0.35  SPASS allocated 63095 KBytes.
% 0.13/0.35  SPASS spent	0:00:00.05 on the problem.
% 0.13/0.35  		0:00:00.03 for the input.
% 0.13/0.35  		0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.35  		0:00:00.00 for inferences.
% 0.13/0.35  		0:00:00.00 for the backtracking.
% 0.13/0.35  		0:00:00.00 for the reduction.
% 0.13/0.35  
% 0.13/0.35  
% 0.13/0.35  Here is a proof with depth 2, length 10 :
% 0.13/0.35  % SZS output start Refutation
% See solution above
% 0.13/0.35  Formulae used in the proof : cls_Message_Oparts__subset__iff_0 cls_Message_Oparts__subset__iff_1 cls_Set_Oinsert__subset_2 cls_Set_Osubset__refl_0 cls_conjecture_0 cls_conjecture_1
% 0.13/0.35  
%------------------------------------------------------------------------------