%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SCT002-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 : Mon Jul 18 22:12:57 EDT 2022

% Result   : Unsatisfiable 0.62s 0.83s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   7 unt;   0 nHn;  11 RR)
%            Number of literals    :   16 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(553,axiom,
    ( ~ c_Relation_Otrans(u,v)
    | equal(c_Transitive__Closure_Otrancl(u,v),u) ),
    file('SCT002-1.p',unknown),
    [] ).

cnf(615,axiom,
    ( ~ hBOOL(c_in(c_Pair(u,v,w,w),x,tc_prod(w,w)))
    | ~ hBOOL(c_in(c_Pair(v,y,w,w),x,tc_prod(w,w)))
    | hBOOL(c_in(c_Pair(u,y,w,w),c_Transitive__Closure_Otrancl(x,w),tc_prod(w,w))) ),
    file('SCT002-1.p',unknown),
    [] ).

cnf(673,axiom,
    c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
    file('SCT002-1.p',unknown),
    [] ).

cnf(674,axiom,
    ~ hBOOL(c_in(c_Pair(u,u,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('SCT002-1.p',unknown),
    [] ).

cnf(675,axiom,
    hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('SCT002-1.p',unknown),
    [] ).

cnf(676,axiom,
    hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('SCT002-1.p',unknown),
    [] ).

cnf(733,plain,
    equal(c_Transitive__Closure_Otrancl(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_L),
    inference(res,[status(thm),theory(equality)],[673,553]),
    [iquote('0:Res:673.0,553.0')] ).

cnf(857,plain,
    ( ~ hBOOL(c_in(c_Pair(u,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(u,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Transitive__Closure_Otrancl(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(res,[status(thm),theory(equality)],[676,615]),
    [iquote('0:Res:676.0,615.0')] ).

cnf(1019,plain,
    ( ~ hBOOL(c_in(c_Pair(u,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(u,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(rew,[status(thm),theory(equality)],[733,857]),
    [iquote('0:Rew:733.0,857.1')] ).

cnf(1054,plain,
    hBOOL(c_in(c_Pair(v_y,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(res,[status(thm),theory(equality)],[675,1019]),
    [iquote('0:Res:675.0,1019.0')] ).

cnf(1108,plain,
    $false,
    inference(mrr,[status(thm)],[1054,674]),
    [iquote('0:MRR:1054.0,674.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SCT002-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  2 06:52:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.62/0.83  
% 0.62/0.83  SPASS V 3.9 
% 0.62/0.83  SPASS beiseite: Proof found.
% 0.62/0.83  % SZS status Theorem
% 0.62/0.83  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.62/0.83  SPASS derived 270 clauses, backtracked 0 clauses, performed 0 splits and kept 728 clauses.
% 0.62/0.83  SPASS allocated 77469 KBytes.
% 0.62/0.83  SPASS spent	0:00:00.46 on the problem.
% 0.62/0.83  		0:00:00.06 for the input.
% 0.62/0.83  		0:00:00.00 for the FLOTTER CNF translation.
% 0.62/0.83  		0:00:00.00 for inferences.
% 0.62/0.83  		0:00:00.00 for the backtracking.
% 0.62/0.83  		0:00:00.15 for the reduction.
% 0.62/0.83  
% 0.62/0.83  
% 0.62/0.83  Here is a proof with depth 2, length 11 :
% 0.62/0.83  % SZS output start Refutation
% See solution above
% 0.62/0.83  Formulae used in the proof : cls_trancl__id_0 cls_r__r__into__trancl_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4
% 0.62/0.83  
%------------------------------------------------------------------------------