%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL809-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 14:40:12 EDT 2022

% Result   : Unsatisfiable 0.61s 0.84s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   8 unt;   0 nHn;   9 RR)
%            Number of literals    :   10 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1170,axiom,
    equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
    file('LCL809-1.p',unknown),
    [] ).

cnf(1198,axiom,
    equal(v_i____,v_n____),
    file('LCL809-1.p',unknown),
    [] ).

cnf(1199,axiom,
    ( ~ c_InductTermi_OIT(u)
    | c_InductTermi_OIT(c_Lambda_Olift(u,v)) ),
    file('LCL809-1.p',unknown),
    [] ).

cnf(1202,axiom,
    c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
    file('LCL809-1.p',unknown),
    [] ).

cnf(1239,axiom,
    ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
    file('LCL809-1.p',unknown),
    [] ).

cnf(1240,plain,
    c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_n____)),
    inference(rew,[status(thm),theory(equality)],[1198,1202]),
    [iquote('0:Rew:1198.0,1202.0')] ).

cnf(1269,plain,
    ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_Osubst(v_b____,v_u____,v_n____),c_Orderings_Obot__class_Obot(tc_nat))),
    inference(rew,[status(thm),theory(equality)],[1198,1239,1170]),
    [iquote('0:Rew:1198.0,1239.0,1170.0,1239.0')] ).

cnf(1424,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_n____)),
    inference(res,[status(thm),theory(equality)],[1199,1269]),
    [iquote('0:Res:1199.1,1269.0')] ).

cnf(1425,plain,
    $false,
    inference(mrr,[status(thm)],[1424,1240]),
    [iquote('0:MRR:1424.0,1240.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL809-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n004.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
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sat Jul  2 21:31:53 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.61/0.84  
% 0.61/0.84  SPASS V 3.9 
% 0.61/0.84  SPASS beiseite: Proof found.
% 0.61/0.84  % SZS status Theorem
% 0.61/0.84  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.61/0.84  SPASS derived 12 clauses, backtracked 0 clauses, performed 0 splits and kept 1036 clauses.
% 0.61/0.84  SPASS allocated 77769 KBytes.
% 0.61/0.84  SPASS spent	0:00:00.47 on the problem.
% 0.61/0.84  		0:00:00.10 for the input.
% 0.61/0.84  		0:00:00.00 for the FLOTTER CNF translation.
% 0.61/0.84  		0:00:00.00 for inferences.
% 0.61/0.84  		0:00:00.00 for the backtracking.
% 0.61/0.84  		0:00:00.26 for the reduction.
% 0.61/0.84  
% 0.61/0.84  
% 0.61/0.84  Here is a proof with depth 1, length 9 :
% 0.61/0.84  % SZS output start Refutation
% See solution above
% 0.61/0.84  Formulae used in the proof : cls_bot__nat__def_0 cls_True_0 cls_lift__IT_0 cls_CHAINED_0 cls_conjecture_0
% 0.61/0.84  
%------------------------------------------------------------------------------