%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL784-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 14:39:56 EDT 2022

% Result   : Unsatisfiable 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (  11 unt;   0 nHn;  11 RR)
%            Number of literals    :   11 (   0 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;  12 con; 0-5 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(221,axiom,
    equal(hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(u)),v),u),v),
    file('LCL784-1.p',unknown),
    [] ).

cnf(245,axiom,
    equal(c_List_Ofoldl(u,v,c_List_Olist_ONil(w),x,w),v),
    file('LCL784-1.p',unknown),
    [] ).

cnf(294,axiom,
    equal(c_List_Olist_ONil(tc_Lambda_OdB),v_rs____),
    file('LCL784-1.p',unknown),
    [] ).

cnf(295,axiom,
    equal(v_i____,v_n____),
    file('LCL784-1.p',unknown),
    [] ).

cnf(296,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    file('LCL784-1.p',unknown),
    [] ).

cnf(317,axiom,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
    file('LCL784-1.p',unknown),
    [] ).

cnf(323,plain,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_n____))),
    inference(rew,[status(thm),theory(equality)],[295,317]),
    [iquote('0:Rew:295.0,317.0')] ).

cnf(390,plain,
    equal(c_List_Ofoldl(u,v,v_rs____,w,tc_Lambda_OdB),v),
    inference(spr,[status(thm),theory(equality)],[294,245]),
    [iquote('0:SpR:294.0,245.0')] ).

cnf(395,plain,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),v_u____),v_n____))),
    inference(rew,[status(thm),theory(equality)],[390,323]),
    [iquote('0:Rew:390.0,323.0')] ).

cnf(396,plain,
    ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    inference(rew,[status(thm),theory(equality)],[221,395]),
    [iquote('0:Rew:221.0,395.0')] ).

cnf(397,plain,
    $false,
    inference(mrr,[status(thm)],[396,296]),
    [iquote('0:MRR:396.0,296.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL784-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n020.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 : Sun Jul  3 02:37:00 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.20/0.50  
% 0.20/0.50  SPASS V 3.9 
% 0.20/0.50  SPASS beiseite: Proof found.
% 0.20/0.50  % SZS status Theorem
% 0.20/0.50  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.50  SPASS derived 43 clauses, backtracked 0 clauses, performed 0 splits and kept 275 clauses.
% 0.20/0.50  SPASS allocated 76287 KBytes.
% 0.20/0.50  SPASS spent	0:00:00.15 on the problem.
% 0.20/0.50  		0:00:00.04 for the input.
% 0.20/0.50  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50  		0:00:00.00 for inferences.
% 0.20/0.50  		0:00:00.00 for the backtracking.
% 0.20/0.50  		0:00:00.06 for the reduction.
% 0.20/0.50  
% 0.20/0.50  
% 0.20/0.50  Here is a proof with depth 1, length 11 :
% 0.20/0.50  % SZS output start Refutation
% See solution above
% 0.20/0.50  Formulae used in the proof : cls_subst__eq_0 cls_foldl__Nil_0 cls_CHAINED_0 cls_CHAINED_0_01 cls_CHAINED_0_02 cls_conjecture_0
% 0.20/0.50  
%------------------------------------------------------------------------------