TSTP Solution File: SET851-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET851-1 : 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 : Tue Jul 19 05:29:16 EDT 2022

% Result   : Unsatisfiable 0.41s 0.59s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   13 (   9 unt;   3 nHn;  13 RR)
%            Number of literals    :   20 (   0 equ;   8 neg)
%            Maximal clause size   :    4 (   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(4,axiom,
    ( ~ c_lessequals(u,v,tc_set(tc_set(w)))
    | c_lessequals(u,c_Zorn_Osucc(x,v,w),tc_set(tc_set(w))) ),
    file('SET851-1.p',unknown),
    [] ).

cnf(6,axiom,
    c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET851-1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
    file('SET851-1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
    file('SET851-1.p',unknown),
    [] ).

cnf(9,axiom,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
    | c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
    file('SET851-1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ c_lessequals(u,v_m,tc_set(tc_set(t_a)))
    | ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | equal(u,v_m)
    | c_lessequals(c_Zorn_Osucc(v_S,u,t_a),v_m,tc_set(tc_set(t_a))) ),
    file('SET851-1.p',unknown),
    [] ).

cnf(320,axiom,
    c_lessequals(u,u,tc_set(v)),
    file('SET851-1.p',unknown),
    [] ).

cnf(1384,plain,
    ( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a)))
    | equal(v_x,v_m) ),
    inference(res,[status(thm),theory(equality)],[6,10]),
    [iquote('0:Res:6.0,10.1')] ).

cnf(1427,plain,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
    inference(res,[status(thm),theory(equality)],[4,8]),
    [iquote('0:Res:4.1,8.0')] ).

cnf(1438,plain,
    c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
    inference(mrr,[status(thm)],[9,1427]),
    [iquote('0:MRR:9.0,1427.0')] ).

cnf(1439,plain,
    equal(v_x,v_m),
    inference(mrr,[status(thm)],[1384,1438,7]),
    [iquote('0:MRR:1384.0,1384.1,1438.0,7.0')] ).

cnf(1442,plain,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
    inference(rew,[status(thm),theory(equality)],[1439,8]),
    [iquote('0:Rew:1439.0,8.0')] ).

cnf(1454,plain,
    $false,
    inference(mrr,[status(thm)],[1442,320]),
    [iquote('0:MRR:1442.0,320.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SET851-1 : TPTP v8.1.0. Released v3.2.0.
% 0.02/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 16:38:32 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.41/0.59  
% 0.41/0.59  SPASS V 3.9 
% 0.41/0.59  SPASS beiseite: Proof found.
% 0.41/0.59  % SZS status Theorem
% 0.41/0.59  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.41/0.59  SPASS derived 40 clauses, backtracked 0 clauses, performed 0 splits and kept 1350 clauses.
% 0.41/0.59  SPASS allocated 77794 KBytes.
% 0.41/0.59  SPASS spent	0:00:00.24 on the problem.
% 0.41/0.59  		0:00:00.08 for the input.
% 0.41/0.59  		0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.59  		0:00:00.00 for inferences.
% 0.41/0.59  		0:00:00.00 for the backtracking.
% 0.41/0.59  		0:00:00.07 for the reduction.
% 0.41/0.59  
% 0.41/0.59  
% 0.41/0.59  Here is a proof with depth 1, length 13 :
% 0.41/0.59  % SZS output start Refutation
% See solution above
% 0.41/0.59  Formulae used in the proof : cls_Zorn_Osucc__trans_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_Set_Osubset__refl_0
% 0.41/0.59  
%------------------------------------------------------------------------------