%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET859-1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 05:29:22 EDT 2022

% Result   : Unsatisfiable 0.47s 0.67s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :   10 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_lessequals(u,v,tc_set(w))
    | ~ c_lessequals(v,x,tc_set(w))
    | c_lessequals(u,x,tc_set(w)) ),
    file('SET859-1.p',unknown),
    [] ).

cnf(2,axiom,
    c_lessequals(u,c_Zorn_Osucc(v,u,w),tc_set(tc_set(w))),
    file('SET859-1.p',unknown),
    [] ).

cnf(10,axiom,
    c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))),
    file('SET859-1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
    file('SET859-1.p',unknown),
    [] ).

cnf(1472,plain,
    ( ~ c_lessequals(u,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
    inference(res,[status(thm),theory(equality)],[10,1]),
    [iquote('0:Res:10.0,1.0')] ).

cnf(1485,plain,
    ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))),
    inference(res,[status(thm),theory(equality)],[1472,11]),
    [iquote('0:Res:1472.1,11.0')] ).

cnf(1557,plain,
    $false,
    inference(mrr,[status(thm)],[1485,2]),
    [iquote('0:MRR:1485.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET859-1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n010.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 : Mon Jul 11 10:15:45 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.47/0.67  
% 0.47/0.67  SPASS V 3.9 
% 0.47/0.67  SPASS beiseite: Proof found.
% 0.47/0.67  % SZS status Theorem
% 0.47/0.67  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.47/0.67  SPASS derived 135 clauses, backtracked 0 clauses, performed 0 splits and kept 1388 clauses.
% 0.47/0.67  SPASS allocated 77793 KBytes.
% 0.47/0.67  SPASS spent	0:00:00.30 on the problem.
% 0.47/0.67  		0:00:00.08 for the input.
% 0.47/0.67  		0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.67  		0:00:00.00 for inferences.
% 0.47/0.67  		0:00:00.00 for the backtracking.
% 0.47/0.67  		0:00:00.07 for the reduction.
% 0.47/0.67  
% 0.47/0.67  
% 0.47/0.67  Here is a proof with depth 2, length 7 :
% 0.47/0.67  % SZS output start Refutation
% See solution above
% 0.47/0.67  Formulae used in the proof : cls_Set_Osubset__trans_0 cls_Zorn_OAbrial__axiom1_0 cls_conjecture_2 cls_conjecture_3
% 0.47/0.67  
%------------------------------------------------------------------------------