%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 05:29:19 EDT 2022

% Result   : Unsatisfiable 0.21s 0.42s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    6 (   4 unt;   0 nHn;   6 RR)
%            Number of literals    :    9 (   0 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_lessequals(u,v,tc_set(w))
    | ~ c_lessequals(v,u,tc_set(w))
    | equal(u,v) ),
    file('SET855-2.p',unknown),
    [] ).

cnf(2,axiom,
    c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    file('SET855-2.p',unknown),
    [] ).

cnf(3,axiom,
    c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
    file('SET855-2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(c_Union(v_Y,tc_set(t_a)),v_n),
    file('SET855-2.p',unknown),
    [] ).

cnf(7,plain,
    ( ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | equal(c_Union(v_Y,tc_set(t_a)),v_n) ),
    inference(res,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Res:3.0,1.0')] ).

cnf(9,plain,
    $false,
    inference(mrr,[status(thm)],[7,2,4]),
    [iquote('0:MRR:7.0,7.1,2.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 600
% 0.13/0.36  % DateTime : Sun Jul 10 10:40:52 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.21/0.42  
% 0.21/0.42  SPASS V 3.9 
% 0.21/0.42  SPASS beiseite: Proof found.
% 0.21/0.42  % SZS status Theorem
% 0.21/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.42  SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 5 clauses.
% 0.21/0.42  SPASS allocated 63084 KBytes.
% 0.21/0.42  SPASS spent	0:00:00.05 on the problem.
% 0.21/0.42  		0:00:00.03 for the input.
% 0.21/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42  		0:00:00.00 for inferences.
% 0.21/0.42  		0:00:00.00 for the backtracking.
% 0.21/0.42  		0:00:00.00 for the reduction.
% 0.21/0.42  
% 0.21/0.42  
% 0.21/0.42  Here is a proof with depth 1, length 6 :
% 0.21/0.42  % SZS output start Refutation
% See solution above
% 0.21/0.42  Formulae used in the proof : cls_Set_Osubset__antisym_0 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4
% 0.21/0.42  
%------------------------------------------------------------------------------