%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL762-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 14:39:44 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   5 unt;   0 nHn;   5 RR)
%            Number of literals    :    5 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-5 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(396,axiom,
    equal(c_List_Ofoldl(u,v,c_List_Olist_ONil(w),x,w),v),
    file('LCL762-1.p',unknown),
    [] ).

cnf(421,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file('LCL762-1.p',unknown),
    [] ).

cnf(422,axiom,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
    file('LCL762-1.p',unknown),
    [] ).

cnf(424,plain,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
    inference(rew,[status(thm),theory(equality)],[396,421]),
    [iquote('0:Rew:396.0,421.0')] ).

cnf(425,plain,
    $false,
    inference(mrr,[status(thm)],[424,422]),
    [iquote('0:MRR:424.0,422.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : LCL762-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n012.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat Jul  2 14:19:47 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.48  
% 0.19/0.48  SPASS V 3.9 
% 0.19/0.48  SPASS beiseite: Proof found.
% 0.19/0.48  % SZS status Theorem
% 0.19/0.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.48  SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 72 clauses.
% 0.19/0.48  SPASS allocated 76362 KBytes.
% 0.19/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.19/0.48  		0:00:00.05 for the input.
% 0.19/0.48  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48  		0:00:00.00 for inferences.
% 0.19/0.48  		0:00:00.00 for the backtracking.
% 0.19/0.48  		0:00:00.02 for the reduction.
% 0.19/0.48  
% 0.19/0.48  
% 0.19/0.48  Here is a proof with depth 0, length 5 :
% 0.19/0.48  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : cls_foldl__Nil_0 cls_conjecture_0 cls_conjecture_1
% 0.19/0.48  
%------------------------------------------------------------------------------