%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL773-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 14:39:50 EDT 2022

% Result   : Unsatisfiable 0.53s 0.72s
% 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 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1019,axiom,
    equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
    file('LCL773-1.p',unknown),
    [] ).

cnf(1060,axiom,
    ( ~ c_InductTermi_OIT(u)
    | c_InductTermi_OIT(c_Lambda_Osubst(u,c_Lambda_OdB_OVar(v),w)) ),
    file('LCL773-1.p',unknown),
    [] ).

cnf(1101,axiom,
    c_InductTermi_OIT(v_r),
    file('LCL773-1.p',unknown),
    [] ).

cnf(1103,axiom,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
    file('LCL773-1.p',unknown),
    [] ).

cnf(1128,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_Orderings_Obot__class_Obot(tc_nat))),
    inference(rew,[status(thm),theory(equality)],[1019,1103]),
    [iquote('0:Rew:1019.0,1103.0')] ).

cnf(1276,plain,
    ~ c_InductTermi_OIT(v_r),
    inference(res,[status(thm),theory(equality)],[1060,1128]),
    [iquote('0:Res:1060.1,1128.0')] ).

cnf(1277,plain,
    $false,
    inference(mrr,[status(thm)],[1276,1101]),
    [iquote('0:MRR:1276.0,1101.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : LCL773-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n006.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 : Sat Jul  2 19:32:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.53/0.72  
% 0.53/0.72  SPASS V 3.9 
% 0.53/0.72  SPASS beiseite: Proof found.
% 0.53/0.72  % SZS status Theorem
% 0.53/0.72  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.53/0.72  SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 919 clauses.
% 0.53/0.72  SPASS allocated 77515 KBytes.
% 0.53/0.72  SPASS spent	0:00:00.37 on the problem.
% 0.53/0.72  		0:00:00.09 for the input.
% 0.53/0.72  		0:00:00.00 for the FLOTTER CNF translation.
% 0.53/0.72  		0:00:00.00 for inferences.
% 0.53/0.72  		0:00:00.00 for the backtracking.
% 0.53/0.72  		0:00:00.19 for the reduction.
% 0.53/0.72  
% 0.53/0.72  
% 0.53/0.72  Here is a proof with depth 1, length 7 :
% 0.53/0.72  % SZS output start Refutation
% See solution above
% 0.53/0.72  Formulae used in the proof : cls_bot__nat__def_0 cls_subst__Var__IT_0 cls_conjecture_0 cls_conjecture_2
% 0.53/0.72  
%------------------------------------------------------------------------------