%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL798-1 : 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 14:40:05 EDT 2022

% Result   : Unsatisfiable 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   9 unt;   0 nHn;  12 RR)
%            Number of literals    :   18 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;  12 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(62,axiom,
    equal(v_i____,v_n____),
    file('LCL798-1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ c_InductTermi_OIT(u)
    | ~ c_Type_Otyping(v,u,v_T____)
    | ~ c_Type_Otyping(c_Type_Oshift(v,w,v_T____,tc_Type_Otype),v_a____,x)
    | c_InductTermi_OIT(c_Lambda_Osubst(v_a____,u,w)) ),
    file('LCL798-1.p',unknown),
    [] ).

cnf(71,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    file('LCL798-1.p',unknown),
    [] ).

cnf(72,axiom,
    c_InductTermi_OIT(v_u____),
    file('LCL798-1.p',unknown),
    [] ).

cnf(73,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
    file('LCL798-1.p',unknown),
    [] ).

cnf(80,axiom,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
    file('LCL798-1.p',unknown),
    [] ).

cnf(81,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_n____)),
    inference(rew,[status(thm),theory(equality)],[62,80]),
    [iquote('0:Rew:62.0,80.0')] ).

cnf(82,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
    inference(rew,[status(thm),theory(equality)],[62,73]),
    [iquote('0:Rew:62.0,73.0')] ).

cnf(539,plain,
    ( ~ c_InductTermi_OIT(u)
    | ~ c_Type_Otyping(v_e____,u,v_T____)
    | c_InductTermi_OIT(c_Lambda_Osubst(v_a____,u,v_n____)) ),
    inference(res,[status(thm),theory(equality)],[82,70]),
    [iquote('0:Res:82.0,70.2')] ).

cnf(554,plain,
    ( ~ c_InductTermi_OIT(v_u____)
    | ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
    inference(res,[status(thm),theory(equality)],[539,81]),
    [iquote('0:Res:539.2,81.0')] ).

cnf(555,plain,
    ~ c_Type_Otyping(v_e____,v_u____,v_T____),
    inference(ssi,[status(thm)],[554,72]),
    [iquote('0:SSi:554.0,72.0')] ).

cnf(556,plain,
    $false,
    inference(mrr,[status(thm)],[555,71]),
    [iquote('0:MRR:555.0,71.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL798-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n012.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 05:11:31 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.49  
% 0.19/0.49  SPASS V 3.9 
% 0.19/0.49  SPASS beiseite: Proof found.
% 0.19/0.49  % SZS status Theorem
% 0.19/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.49  SPASS derived 462 clauses, backtracked 0 clauses, performed 0 splits and kept 301 clauses.
% 0.19/0.49  SPASS allocated 76244 KBytes.
% 0.19/0.49  SPASS spent	0:00:00.14 on the problem.
% 0.19/0.49  		0:00:00.04 for the input.
% 0.19/0.49  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49  		0:00:00.01 for inferences.
% 0.19/0.49  		0:00:00.00 for the backtracking.
% 0.19/0.49  		0:00:00.06 for the reduction.
% 0.19/0.49  
% 0.19/0.49  
% 0.19/0.49  Here is a proof with depth 2, length 12 :
% 0.19/0.49  % SZS output start Refutation
% See solution above
% 0.19/0.49  Formulae used in the proof : cls_True_0 cls_CHAINED_0 cls_CHAINED_0_01 cls_CHAINED_0_02 cls_CHAINED_0_03 cls_conjecture_0
% 0.19/0.49  
%------------------------------------------------------------------------------