%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET855-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 0.45s 0.62s
% Output   : Refutation 0.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   5 unt;   2 nHn;   8 RR)
%            Number of literals    :   12 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   3 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(12,axiom,
    c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    file('SET855-1.p',unknown),
    [] ).

cnf(13,axiom,
    c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
    file('SET855-1.p',unknown),
    [] ).

cnf(14,axiom,
    ~ equal(c_Union(v_Y,tc_set(t_a)),v_n),
    file('SET855-1.p',unknown),
    [] ).

cnf(316,axiom,
    ( ~ c_lessequals(u,v,tc_set(w))
    | ~ c_less(v,u,tc_set(w)) ),
    file('SET855-1.p',unknown),
    [] ).

cnf(318,axiom,
    ( ~ c_lessequals(u,v,tc_set(w))
    | equal(u,v)
    | c_less(u,v,tc_set(w)) ),
    file('SET855-1.p',unknown),
    [] ).

cnf(1485,plain,
    ( c_less(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
    | equal(c_Union(v_Y,tc_set(t_a)),v_n) ),
    inference(res,[status(thm),theory(equality)],[13,318]),
    [iquote('0:Res:13.0,318.0')] ).

cnf(1503,plain,
    ~ c_less(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
    inference(res,[status(thm),theory(equality)],[12,316]),
    [iquote('0:Res:12.0,316.1')] ).

cnf(1575,plain,
    $false,
    inference(mrr,[status(thm)],[1485,1503,14]),
    [iquote('0:MRR:1485.0,1485.1,1503.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SET855-1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n022.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 14:11:10 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.45/0.62  
% 0.45/0.62  SPASS V 3.9 
% 0.45/0.62  SPASS beiseite: Proof found.
% 0.45/0.62  % SZS status Theorem
% 0.45/0.62  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.45/0.62  SPASS derived 82 clauses, backtracked 0 clauses, performed 0 splits and kept 1352 clauses.
% 0.45/0.62  SPASS allocated 77804 KBytes.
% 0.45/0.62  SPASS spent	0:00:00.27 on the problem.
% 0.45/0.62  		0:00:00.09 for the input.
% 0.45/0.62  		0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.62  		0:00:00.00 for inferences.
% 0.45/0.62  		0:00:00.00 for the backtracking.
% 0.45/0.62  		0:00:00.08 for the reduction.
% 0.45/0.62  
% 0.45/0.62  
% 0.45/0.62  Here is a proof with depth 1, length 8 :
% 0.45/0.62  % SZS output start Refutation
% See solution above
% 0.45/0.62  Formulae used in the proof : cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_Set_OpsubsetE_0 cls_Set_OpsubsetI_0
% 0.45/0.62  
%------------------------------------------------------------------------------