%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL851-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 : Sun Jul 17 14:40:35 EDT 2022

% Result   : Unsatisfiable 0.53s 0.76s
% Output   : Refutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :    8 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;  11 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(855,axiom,
    equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
    file('LCL851-1.p',unknown),
    [] ).

cnf(901,axiom,
    ( ~ c_Type_Otyping(u,v,w)
    | c_Type_Otyping(c_Type_Oshift(u,x,y,tc_Type_Otype),c_Lambda_Olift(v,x),w) ),
    file('LCL851-1.p',unknown),
    [] ).

cnf(905,axiom,
    c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
    file('LCL851-1.p',unknown),
    [] ).

cnf(946,axiom,
    ~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____),
    file('LCL851-1.p',unknown),
    [] ).

cnf(1022,plain,
    ~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_Orderings_Obot__class_Obot(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_Orderings_Obot__class_Obot(tc_nat)),v_Ta____),
    inference(rew,[status(thm),theory(equality)],[855,946]),
    [iquote('0:Rew:855.0,946.0')] ).

cnf(1178,plain,
    ~ c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
    inference(res,[status(thm),theory(equality)],[901,1022]),
    [iquote('0:Res:901.1,1022.0')] ).

cnf(1179,plain,
    $false,
    inference(mrr,[status(thm)],[1178,905]),
    [iquote('0:MRR:1178.0,905.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL851-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n009.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 : Mon Jul  4 06:12:22 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.53/0.76  
% 0.53/0.76  SPASS V 3.9 
% 0.53/0.76  SPASS beiseite: Proof found.
% 0.53/0.76  % SZS status Theorem
% 0.53/0.76  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.53/0.76  SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 761 clauses.
% 0.53/0.76  SPASS allocated 77434 KBytes.
% 0.53/0.76  SPASS spent	0:00:00.40 on the problem.
% 0.53/0.76  		0:00:00.08 for the input.
% 0.53/0.76  		0:00:00.00 for the FLOTTER CNF translation.
% 0.53/0.76  		0:00:00.00 for inferences.
% 0.53/0.76  		0:00:00.00 for the backtracking.
% 0.53/0.76  		0:00:00.24 for the reduction.
% 0.53/0.76  
% 0.53/0.76  
% 0.53/0.76  Here is a proof with depth 1, length 7 :
% 0.53/0.76  % SZS output start Refutation
% See solution above
% 0.53/0.76  Formulae used in the proof : cls_bot__nat__def_0 cls_lift__type_0 cls_App_I3_J_0 cls_conjecture_0
% 0.53/0.76  
%------------------------------------------------------------------------------