%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL755-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 14:39:40 EDT 2022

% Result   : Unsatisfiable 0.41s 0.60s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   4 unt;   0 nHn;   5 RR)
%            Number of literals    :    6 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(710,axiom,
    ( ~ c_InductTermi_OIT(u)
    | c_InductTermi_OIT(c_Lambda_OdB_OAbs(u)) ),
    file('LCL755-1.p',unknown),
    [] ).

cnf(754,axiom,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(u),v)),
    file('LCL755-1.p',unknown),
    [] ).

cnf(755,axiom,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    file('LCL755-1.p',unknown),
    [] ).

cnf(820,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
    inference(res,[status(thm),theory(equality)],[710,755]),
    [iquote('0:Res:710.1,755.0')] ).

cnf(821,plain,
    $false,
    inference(mrr,[status(thm)],[820,754]),
    [iquote('0:MRR:820.0,754.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL755-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n024.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 : Mon Jul  4 18:36:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.41/0.60  
% 0.41/0.60  SPASS V 3.9 
% 0.41/0.60  SPASS beiseite: Proof found.
% 0.41/0.60  % SZS status Theorem
% 0.41/0.60  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.41/0.60  SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 600 clauses.
% 0.41/0.60  SPASS allocated 76867 KBytes.
% 0.41/0.60  SPASS spent	0:00:00.25 on the problem.
% 0.41/0.60  		0:00:00.06 for the input.
% 0.41/0.60  		0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.60  		0:00:00.00 for inferences.
% 0.41/0.60  		0:00:00.00 for the backtracking.
% 0.41/0.60  		0:00:00.11 for the reduction.
% 0.41/0.60  
% 0.41/0.60  
% 0.41/0.60  Here is a proof with depth 1, length 5 :
% 0.41/0.60  % SZS output start Refutation
% See solution above
% 0.41/0.60  Formulae used in the proof : cls_Lambda_0 cls_conjecture_1 cls_conjecture_2
% 0.41/0.60  
%------------------------------------------------------------------------------