%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL856-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 14:40:37 EDT 2022

% Result   : Unsatisfiable 0.19s 0.46s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :    9 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(138,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
    | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),u,tc_Lambda_OdB) ),
    file('LCL856-1.p',unknown),
    [] ).

cnf(170,axiom,
    ( ~ c_Type_Otyping(u,v,w)
    | hBOOL(hAPP(c_InductTermi_OIT,v)) ),
    file('LCL856-1.p',unknown),
    [] ).

cnf(186,axiom,
    c_Type_Otyping(v_e,v_t,v_T),
    file('LCL856-1.p',unknown),
    [] ).

cnf(187,axiom,
    ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
    file('LCL856-1.p',unknown),
    [] ).

cnf(197,plain,
    hBOOL(hAPP(c_InductTermi_OIT,v_t)),
    inference(res,[status(thm),theory(equality)],[186,170]),
    [iquote('0:Res:186.0,170.0')] ).

cnf(199,plain,
    ~ hBOOL(hAPP(c_InductTermi_OIT,v_t)),
    inference(res,[status(thm),theory(equality)],[138,187]),
    [iquote('0:Res:138.1,187.0')] ).

cnf(209,plain,
    $false,
    inference(mrr,[status(thm)],[199,197]),
    [iquote('0:MRR:199.0,197.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : LCL856-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul  3 12:40:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  
% 0.19/0.46  SPASS V 3.9 
% 0.19/0.46  SPASS beiseite: Proof found.
% 0.19/0.46  % SZS status Theorem
% 0.19/0.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.46  SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 171 clauses.
% 0.19/0.46  SPASS allocated 75951 KBytes.
% 0.19/0.46  SPASS spent	0:00:00.10 on the problem.
% 0.19/0.46  		0:00:00.04 for the input.
% 0.19/0.46  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46  		0:00:00.00 for inferences.
% 0.19/0.46  		0:00:00.00 for the backtracking.
% 0.19/0.46  		0:00:00.02 for the reduction.
% 0.19/0.46  
% 0.19/0.46  
% 0.19/0.46  Here is a proof with depth 1, length 7 :
% 0.19/0.46  % SZS output start Refutation
% See solution above
% 0.19/0.46  Formulae used in the proof : cls_IT__implies__termi_0 cls_type__implies__IT_0 cls_conjecture_0 cls_conjecture_1
% 0.19/0.46  
%------------------------------------------------------------------------------