%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET841-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 05:29:08 EDT 2022

% Result   : Unsatisfiable 0.47s 0.65s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   12 (  10 unt;   1 nHn;  12 RR)
%            Number of literals    :   19 (   0 equ;   9 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_lessequals(u,v,tc_set(tc_set(w)))
    | ~ c_in(v,c_Zorn_OTFin(x,w),tc_set(tc_set(w)))
    | ~ c_in(u,c_Zorn_OTFin(x,w),tc_set(tc_set(w)))
    | equal(u,v)
    | c_lessequals(c_Zorn_Osucc(x,u,w),v,tc_set(tc_set(w))) ),
    file('SET841-1.p',unknown),
    [] ).

cnf(2,axiom,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET841-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m),
    file('SET841-1.p',unknown),
    [] ).

cnf(4,axiom,
    c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET841-1.p',unknown),
    [] ).

cnf(5,axiom,
    c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
    file('SET841-1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
    file('SET841-1.p',unknown),
    [] ).

cnf(316,axiom,
    c_lessequals(u,u,tc_set(v)),
    file('SET841-1.p',unknown),
    [] ).

cnf(1421,plain,
    ( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
    | equal(v_x,v_m) ),
    inference(res,[status(thm),theory(equality)],[1,6]),
    [iquote('0:Res:1.3,6.0')] ).

cnf(1433,plain,
    equal(v_x,v_m),
    inference(mrr,[status(thm)],[1421,4,2,5]),
    [iquote('0:MRR:1421.0,1421.1,1421.2,4.0,2.0,5.0')] ).

cnf(1436,plain,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
    inference(rew,[status(thm),theory(equality)],[1433,6]),
    [iquote('0:Rew:1433.0,6.0')] ).

cnf(1447,plain,
    ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))),
    inference(rew,[status(thm),theory(equality)],[3,1436]),
    [iquote('0:Rew:3.0,1436.0')] ).

cnf(1448,plain,
    $false,
    inference(mrr,[status(thm)],[1447,316]),
    [iquote('0:MRR:1447.0,316.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET841-1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n013.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 : Sun Jul 10 15:50:59 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.47/0.65  
% 0.47/0.65  SPASS V 3.9 
% 0.47/0.65  SPASS beiseite: Proof found.
% 0.47/0.65  % SZS status Theorem
% 0.47/0.65  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.47/0.65  SPASS derived 37 clauses, backtracked 0 clauses, performed 0 splits and kept 1348 clauses.
% 0.47/0.65  SPASS allocated 77773 KBytes.
% 0.47/0.65  SPASS spent	0:00:00.29 on the problem.
% 0.47/0.65  		0:00:00.09 for the input.
% 0.47/0.65  		0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.65  		0:00:00.00 for inferences.
% 0.47/0.65  		0:00:00.00 for the backtracking.
% 0.47/0.65  		0:00:00.10 for the reduction.
% 0.47/0.65  
% 0.47/0.65  
% 0.47/0.65  Here is a proof with depth 1, length 12 :
% 0.47/0.65  % SZS output start Refutation
% See solution above
% 0.47/0.65  Formulae used in the proof : cls_Zorn_OTFin__subsetD_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_Set_Osubset__refl_0
% 0.47/0.65  
%------------------------------------------------------------------------------