%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV240-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 21:41:44 EDT 2022

% Result   : Unsatisfiable 8.52s 8.70s
% Output   : Refutation 8.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   5 unt;   2 nHn;  12 RR)
%            Number of literals    :   20 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   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(1,axiom,
    ( ~ c_lessequals(c_Message_Oanalz(u),c_Message_Oanalz(v),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Oanalz(w),c_Message_Oanalz(x),tc_set(tc_Message_Omsg))
    | c_lessequals(c_Message_Oanalz(c_union(u,w,tc_Message_Omsg)),c_Message_Oanalz(c_union(v,x,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
    file('SWV240-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ c_lessequals(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Oanalz(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
    file('SWV240-1.p',unknown),
    [] ).

cnf(112,axiom,
    ( c_lessequals(u,v,tc_set(w))
    | c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
    file('SWV240-1.p',unknown),
    [] ).

cnf(113,axiom,
    ( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
    | c_lessequals(u,v,tc_set(w)) ),
    file('SWV240-1.p',unknown),
    [] ).

cnf(115,axiom,
    c_lessequals(u,u,tc_set(v)),
    file('SWV240-1.p',unknown),
    [] ).

cnf(1380,axiom,
    ( ~ c_in(u,v,tc_Message_Omsg)
    | c_in(u,c_Message_Oanalz(v),tc_Message_Omsg) ),
    file('SWV240-1.p',unknown),
    [] ).

cnf(1412,plain,
    ( ~ c_lessequals(c_Message_Oanalz(v_H),c_Message_Oanalz(v_H),tc_set(tc_Message_Omsg))
    | ~ c_lessequals(c_Message_Oanalz(v_G),c_Message_Oanalz(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) ),
    inference(res,[status(thm),theory(equality)],[1,3]),
    [iquote('0:Res:1.2,3.0')] ).

cnf(1414,plain,
    ~ c_lessequals(c_Message_Oanalz(v_G),c_Message_Oanalz(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),
    inference(mrr,[status(thm)],[1412,115]),
    [iquote('0:MRR:1412.0,115.0')] ).

cnf(1841,plain,
    ( ~ c_in(c_Main_OsubsetI__1(u,c_Message_Oanalz(v),tc_Message_Omsg),v,tc_Message_Omsg)
    | c_lessequals(u,c_Message_Oanalz(v),tc_set(tc_Message_Omsg)) ),
    inference(res,[status(thm),theory(equality)],[1380,113]),
    [iquote('0:Res:1380.1,113.0')] ).

cnf(17334,plain,
    ( c_lessequals(u,c_Message_Oanalz(u),tc_set(tc_Message_Omsg))
    | c_lessequals(u,c_Message_Oanalz(u),tc_set(tc_Message_Omsg)) ),
    inference(res,[status(thm),theory(equality)],[112,1841]),
    [iquote('0:Res:112.1,1841.0')] ).

cnf(17348,plain,
    c_lessequals(u,c_Message_Oanalz(u),tc_set(tc_Message_Omsg)),
    inference(obv,[status(thm),theory(equality)],[17334]),
    [iquote('0:Obv:17334.0')] ).

cnf(17349,plain,
    $false,
    inference(unc,[status(thm)],[17348,1414]),
    [iquote('0:UnC:17348.0,1414.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV240-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n027.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 : Thu Jun 16 00:14:35 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 8.52/8.70  
% 8.52/8.70  SPASS V 3.9 
% 8.52/8.70  SPASS beiseite: Proof found.
% 8.52/8.70  % SZS status Theorem
% 8.52/8.70  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 8.52/8.70  SPASS derived 13084 clauses, backtracked 0 clauses, performed 0 splits and kept 7154 clauses.
% 8.52/8.70  SPASS allocated 91873 KBytes.
% 8.52/8.70  SPASS spent	0:00:08.07 on the problem.
% 8.52/8.70  		0:00:00.09 for the input.
% 8.52/8.70  		0:00:00.00 for the FLOTTER CNF translation.
% 8.52/8.70  		0:00:00.28 for inferences.
% 8.52/8.70  		0:00:00.00 for the backtracking.
% 8.52/8.70  		0:00:07.32 for the reduction.
% 8.52/8.70  
% 8.52/8.70  
% 8.52/8.70  Here is a proof with depth 2, length 12 :
% 8.52/8.70  % SZS output start Refutation
% See solution above
% 8.52/8.70  Formulae used in the proof : cls_Message_Oanalz__subset__cong_0 cls_conjecture_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_Set_Osubset__refl_0 cls_Message_Oanalz_OInj_0
% 8.52/8.70  
%------------------------------------------------------------------------------