%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET845-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 05:29:12 EDT 2022

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   18 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_in(u,v,tc_set(w))
    | c_lessequals(u,c_Union(v,w),tc_set(w)) ),
    file('SET845-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ c_lessequals(u,v,tc_set(w))
    | ~ c_lessequals(v,u,tc_set(w))
    | equal(u,v) ),
    file('SET845-2.p',unknown),
    [] ).

cnf(3,axiom,
    c_lessequals(u,c_Zorn_Osucc(v,u,w),tc_set(tc_set(w))),
    file('SET845-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | c_in(c_Zorn_Osucc(v,u,w),c_Zorn_OTFin(v,w),tc_set(tc_set(w))) ),
    file('SET845-2.p',unknown),
    [] ).

cnf(5,axiom,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET845-2.p',unknown),
    [] ).

cnf(6,axiom,
    equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m),
    file('SET845-2.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m),
    file('SET845-2.p',unknown),
    [] ).

cnf(11,plain,
    c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    inference(res,[status(thm),theory(equality)],[5,4]),
    [iquote('0:Res:5.0,4.0')] ).

cnf(14,plain,
    ( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
    inference(spr,[status(thm),theory(equality)],[6,1]),
    [iquote('0:SpR:6.0,1.1')] ).

cnf(16,plain,
    c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
    inference(res,[status(thm),theory(equality)],[11,14]),
    [iquote('0:Res:11.0,14.0')] ).

cnf(18,plain,
    ( ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
    | equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) ),
    inference(res,[status(thm),theory(equality)],[16,2]),
    [iquote('0:Res:16.0,2.0')] ).

cnf(21,plain,
    $false,
    inference(mrr,[status(thm)],[18,3,7]),
    [iquote('0:MRR:18.0,18.1,3.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET845-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n005.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 08:25:22 EDT 2022
% 0.20/0.34  % CPUTime  : 
% 0.20/0.41  
% 0.20/0.41  SPASS V 3.9 
% 0.20/0.41  SPASS beiseite: Proof found.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.41  SPASS derived 12 clauses, backtracked 0 clauses, performed 0 splits and kept 15 clauses.
% 0.20/0.41  SPASS allocated 63105 KBytes.
% 0.20/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.41  		0:00:00.04 for the input.
% 0.20/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41  		0:00:00.00 for inferences.
% 0.20/0.41  		0:00:00.00 for the backtracking.
% 0.20/0.41  		0:00:00.00 for the reduction.
% 0.20/0.41  
% 0.20/0.41  
% 0.20/0.41  Here is a proof with depth 3, length 12 :
% 0.20/0.41  % SZS output start Refutation
% See solution above
% 0.20/0.41  Formulae used in the proof : cls_Set_OUnion__upper_0 cls_Set_Osubset__antisym_0 cls_Zorn_OAbrial__axiom1_0 cls_Zorn_OTFin_OsuccI_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.20/0.41  
%------------------------------------------------------------------------------