%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV857-1 : 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 21:45:24 EDT 2022

% Result   : Unsatisfiable 0.37s 0.60s
% Output   : Refutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   6 unt;   0 nHn;   9 RR)
%            Number of literals    :   13 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(530,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_in(u),v),w))
    | ~ c_lessequals(w,x,tc_fun(u,tc_bool))
    | hBOOL(hAPP(hAPP(c_in(u),v),x)) ),
    file('SWV857-1.p',unknown),
    [] ).

cnf(583,axiom,
    c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
    file('SWV857-1.p',unknown),
    [] ).

cnf(584,axiom,
    hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
    file('SWV857-1.p',unknown),
    [] ).

cnf(585,axiom,
    ~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
    file('SWV857-1.p',unknown),
    [] ).

cnf(586,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Ga))
    | c_Hoare__Mirabelle_Otriple__valid(v_x,u,t_a) ),
    file('SWV857-1.p',unknown),
    [] ).

cnf(631,plain,
    ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga)),
    inference(res,[status(thm),theory(equality)],[586,585]),
    [iquote('0:Res:586.1,585.0')] ).

cnf(754,plain,
    ( ~ c_lessequals(v_tsa,u,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
    | hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),u)) ),
    inference(res,[status(thm),theory(equality)],[584,530]),
    [iquote('0:Res:584.0,530.0')] ).

cnf(806,plain,
    hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_Ga)),
    inference(res,[status(thm),theory(equality)],[583,754]),
    [iquote('0:Res:583.0,754.0')] ).

cnf(818,plain,
    $false,
    inference(mrr,[status(thm)],[806,631]),
    [iquote('0:MRR:806.0,631.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV857-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun 15 12:03:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.37/0.60  
% 0.37/0.60  SPASS V 3.9 
% 0.37/0.60  SPASS beiseite: Proof found.
% 0.37/0.60  % SZS status Theorem
% 0.37/0.60  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.37/0.60  SPASS derived 112 clauses, backtracked 0 clauses, performed 0 splits and kept 555 clauses.
% 0.37/0.60  SPASS allocated 76820 KBytes.
% 0.37/0.60  SPASS spent	0:00:00.24 on the problem.
% 0.37/0.60  		0:00:00.06 for the input.
% 0.37/0.60  		0:00:00.00 for the FLOTTER CNF translation.
% 0.37/0.60  		0:00:00.00 for inferences.
% 0.37/0.60  		0:00:00.00 for the backtracking.
% 0.37/0.60  		0:00:00.11 for the reduction.
% 0.37/0.60  
% 0.37/0.60  
% 0.37/0.60  Here is a proof with depth 2, length 9 :
% 0.37/0.60  % SZS output start Refutation
% See solution above
% 0.37/0.60  Formulae used in the proof : cls_subset__iff_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.37/0.60  
%------------------------------------------------------------------------------