%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL806-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 14:40:10 EDT 2022

% Result   : Unsatisfiable 0.20s 0.61s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   6 unt;   0 nHn;   9 RR)
%            Number of literals    :   15 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :   16 (  16 usr;  14 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(353,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v),u),v_T____))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v),w),v_T____)),v_b____),x))
    | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),u),w))) ),
    file('LCL806-1.p',unknown),
    [] ).

cnf(408,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
    file('LCL806-1.p',unknown),
    [] ).

cnf(409,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
    file('LCL806-1.p',unknown),
    [] ).

cnf(410,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
    file('LCL806-1.p',unknown),
    [] ).

cnf(411,axiom,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
    file('LCL806-1.p',unknown),
    [] ).

cnf(485,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,u),v_xb),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),u),v_xc),v_T____)),v_b____),v)) ),
    inference(res,[status(thm),theory(equality)],[353,411]),
    [iquote('0:Res:353.3,411.0')] ).

cnf(503,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,u),v_xb),v_T____))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),u),v_xc),v_T____)),v_b____),v)) ),
    inference(mrr,[status(thm)],[485,409]),
    [iquote('0:MRR:485.1,409.0')] ).

cnf(534,plain,
    ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
    inference(res,[status(thm),theory(equality)],[408,503]),
    [iquote('0:Res:408.0,503.1')] ).

cnf(545,plain,
    $false,
    inference(mrr,[status(thm)],[534,410]),
    [iquote('0:MRR:534.0,410.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : LCL806-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jul  4 11:41:29 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.20/0.61  
% 0.20/0.61  SPASS V 3.9 
% 0.20/0.61  SPASS beiseite: Proof found.
% 0.20/0.61  % SZS status Theorem
% 0.20/0.61  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.61  SPASS derived 67 clauses, backtracked 0 clauses, performed 0 splits and kept 375 clauses.
% 0.20/0.61  SPASS allocated 78254 KBytes.
% 0.20/0.61  SPASS spent	0:00:00.23 on the problem.
% 0.20/0.61  		0:00:00.06 for the input.
% 0.20/0.61  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.61  		0:00:00.00 for inferences.
% 0.20/0.61  		0:00:00.00 for the backtracking.
% 0.20/0.61  		0:00:00.11 for the reduction.
% 0.20/0.61  
% 0.20/0.61  
% 0.20/0.61  Here is a proof with depth 2, length 9 :
% 0.20/0.61  % SZS output start Refutation
% See solution above
% 0.20/0.61  Formulae used in the proof : cls_Cons_I1_J_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.20/0.61  
%------------------------------------------------------------------------------