%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWW209+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 : Thu Jul 21 01:28:06 EDT 2022

% Result   : Theorem 1.37s 1.57s
% Output   : Refutation 1.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;  11 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(161,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,skc2,skc3),
    file('SWW209+1.p',unknown),
    [] ).

cnf(468,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,u,v)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,u),hAPP(v_f____,v)) ),
    file('SWW209+1.p',unknown),
    [] ).

cnf(469,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,u,v)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,u),hAPP(v_ga____,v)) ),
    file('SWW209+1.p',unknown),
    [] ).

cnf(645,axiom,
    equal(hAPP(hAPP(c_Fun_Ocomp(u,v,w,x),y),z),hAPP(x,hAPP(y,z))),
    file('SWW209+1.p',unknown),
    [] ).

cnf(1123,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),skc2),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),skc3)),
    file('SWW209+1.p',unknown),
    [] ).

cnf(1712,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,skc2)),hAPP(v_f____,hAPP(v_ga____,skc3))),
    inference(rew,[status(thm),theory(equality)],[645,1123]),
    [iquote('0:Rew:645.0,1123.0,645.0,1123.0')] ).

cnf(1799,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,skc2),hAPP(v_ga____,skc3)),
    inference(res,[status(thm),theory(equality)],[161,469]),
    [iquote('0:Res:161.0,469.0')] ).

cnf(1893,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,skc2),hAPP(v_ga____,skc3)),
    inference(res,[status(thm),theory(equality)],[468,1712]),
    [iquote('0:Res:468.1,1712.0')] ).

cnf(1950,plain,
    $false,
    inference(mrr,[status(thm)],[1893,1799]),
    [iquote('0:MRR:1893.0,1799.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWW209+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 Jun  4 08:41:48 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.37/1.57  
% 1.37/1.57  SPASS V 3.9 
% 1.37/1.57  SPASS beiseite: Proof found.
% 1.37/1.57  % SZS status Theorem
% 1.37/1.57  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.37/1.57  SPASS derived 129 clauses, backtracked 0 clauses, performed 0 splits and kept 1330 clauses.
% 1.37/1.57  SPASS allocated 107360 KBytes.
% 1.37/1.57  SPASS spent	0:00:01.20 on the problem.
% 1.37/1.57  		0:00:00.06 for the input.
% 1.37/1.57  		0:00:00.64 for the FLOTTER CNF translation.
% 1.37/1.57  		0:00:00.00 for inferences.
% 1.37/1.57  		0:00:00.00 for the backtracking.
% 1.37/1.57  		0:00:00.35 for the reduction.
% 1.37/1.57  
% 1.37/1.57  
% 1.37/1.57  Here is a proof with depth 1, length 9 :
% 1.37/1.57  % SZS output start Refutation
% See solution above
% 1.37/1.57  Formulae used in the proof : conj_0 fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096 fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096 fact_o__eq__dest__lhs
% 1.37/1.57  
%------------------------------------------------------------------------------