%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL855-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 14:40:36 EDT 2022

% Result   : Unsatisfiable 11.38s 11.57s
% Output   : Refutation 11.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   9 RR)
%            Number of literals    :    9 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(324,axiom,
    equal(c_Lambda_Osubst(c_Lambda_Olift(u,v),w,v),u),
    file('LCL855-1.p',unknown),
    [] ).

cnf(340,axiom,
    equal(c_Lambda_Osubst(c_Lambda_OdB_OVar(u),v,u),v),
    file('LCL855-1.p',unknown),
    [] ).

cnf(343,axiom,
    equal(c_Lambda_OdB_OApp(c_Lambda_Osubst(u,v,w),c_Lambda_Osubst(x,v,w)),c_Lambda_Osubst(c_Lambda_OdB_OApp(u,x),v,w)),
    file('LCL855-1.p',unknown),
    [] ).

cnf(361,axiom,
    c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
    file('LCL855-1.p',unknown),
    [] ).

cnf(384,axiom,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
    file('LCL855-1.p',unknown),
    [] ).

cnf(31242,plain,
    equal(c_Lambda_OdB_OApp(u,c_Lambda_Osubst(v,u,w)),c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(w),v),u,w)),
    inference(spr,[status(thm),theory(equality)],[340,343]),
    [iquote('0:SpR:340.0,343.0')] ).

cnf(31266,plain,
    c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))),
    inference(rew,[status(thm),theory(equality)],[31242,361]),
    [iquote('0:Rew:31242.0,361.0')] ).

cnf(31268,plain,
    c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
    inference(rew,[status(thm),theory(equality)],[324,31266]),
    [iquote('0:Rew:324.0,31266.0')] ).

cnf(31269,plain,
    $false,
    inference(mrr,[status(thm)],[31268,384]),
    [iquote('0:MRR:31268.0,384.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : LCL855-1 : TPTP v8.1.0. Released v4.1.0.
% 0.15/0.15  % Command  : run_spass %d %s
% 0.16/0.37  % Computer : n008.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 600
% 0.16/0.37  % DateTime : Sun Jul  3 07:24:23 EDT 2022
% 0.16/0.37  % CPUTime  : 
% 11.38/11.57  
% 11.38/11.57  SPASS V 3.9 
% 11.38/11.57  SPASS beiseite: Proof found.
% 11.38/11.57  % SZS status Theorem
% 11.38/11.57  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 11.38/11.57  SPASS derived 24956 clauses, backtracked 0 clauses, performed 0 splits and kept 4142 clauses.
% 11.38/11.57  SPASS allocated 92715 KBytes.
% 11.38/11.57  SPASS spent	0:0:10.98 on the problem.
% 11.38/11.57  		0:00:00.04 for the input.
% 11.38/11.57  		0:00:00.00 for the FLOTTER CNF translation.
% 11.38/11.57  		0:00:00.26 for inferences.
% 11.38/11.57  		0:00:00.00 for the backtracking.
% 11.38/11.57  		0:0:10.56 for the reduction.
% 11.38/11.57  
% 11.38/11.57  
% 11.38/11.57  Here is a proof with depth 1, length 9 :
% 11.38/11.57  % SZS output start Refutation
% See solution above
% 11.38/11.57  Formulae used in the proof : cls_subst__lift_0 cls_subst__eq_0 cls_subst__App_0 cls_CHAINED_0 cls_conjecture_0
% 11.38/11.57  
%------------------------------------------------------------------------------