%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL748-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 14:39:37 EDT 2022

% Result   : Unsatisfiable 0.18s 0.54s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(307,axiom,
    equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Suc(u)),
    file('LCL748-1.p',unknown),
    [] ).

cnf(332,axiom,
    equal(c_Lambda_OdB_OAbs(c_Lambda_Olift(u,c_HOL_Oplus__class_Oplus(v,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),c_Lambda_Olift(c_Lambda_OdB_OAbs(u),v)),
    file('LCL748-1.p',unknown),
    [] ).

cnf(339,axiom,
    ( ~ c_InductTermi_OIT(u)
    | c_InductTermi_OIT(c_Lambda_OdB_OAbs(u)) ),
    file('LCL748-1.p',unknown),
    [] ).

cnf(369,axiom,
    c_InductTermi_OIT(c_Lambda_Olift(v_r,u)),
    file('LCL748-1.p',unknown),
    [] ).

cnf(370,axiom,
    ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
    file('LCL748-1.p',unknown),
    [] ).

cnf(374,plain,
    equal(c_Lambda_OdB_OAbs(c_Lambda_Olift(u,c_Suc(v))),c_Lambda_Olift(c_Lambda_OdB_OAbs(u),v)),
    inference(rew,[status(thm),theory(equality)],[307,332]),
    [iquote('0:Rew:307.0,332.0')] ).

cnf(571,plain,
    ( ~ c_InductTermi_OIT(c_Lambda_Olift(u,c_Suc(v)))
    | c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(u),v)) ),
    inference(spr,[status(thm),theory(equality)],[374,339]),
    [iquote('0:SpR:374.0,339.1')] ).

cnf(1969,plain,
    c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),u)),
    inference(sor,[status(thm)],[571,369]),
    [iquote('0:SoR:571.0,369.0')] ).

cnf(1970,plain,
    $false,
    inference(unc,[status(thm)],[1969,370]),
    [iquote('0:UnC:1969.0,370.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LCL748-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n017.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 06:39:12 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.54  
% 0.18/0.54  SPASS V 3.9 
% 0.18/0.54  SPASS beiseite: Proof found.
% 0.18/0.54  % SZS status Theorem
% 0.18/0.54  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.54  SPASS derived 1409 clauses, backtracked 0 clauses, performed 0 splits and kept 452 clauses.
% 0.18/0.54  SPASS allocated 76957 KBytes.
% 0.18/0.54  SPASS spent	0:00:00.19 on the problem.
% 0.18/0.54  		0:00:00.03 for the input.
% 0.18/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.54  		0:00:00.02 for inferences.
% 0.18/0.54  		0:00:00.00 for the backtracking.
% 0.18/0.54  		0:00:00.10 for the reduction.
% 0.18/0.54  
% 0.18/0.54  
% 0.18/0.54  Here is a proof with depth 2, length 9 :
% 0.18/0.54  % SZS output start Refutation
% See solution above
% 0.18/0.54  Formulae used in the proof : cls_Suc__eq__plus1_0 cls_lift_Osimps_I3_J_0 cls_Lambda_0 cls_conjecture_1 cls_conjecture_2
% 0.18/0.54  
%------------------------------------------------------------------------------