%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ANA007-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 14 19:28:38 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   7 unt;   0 nHn;  10 RR)
%            Number of literals    :   13 (   0 equ;   6 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ class_Orderings_Oorder(u)
    | c_lessequals(v,v,u) ),
    file('ANA007-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | equal(c_times(c_1,v,u),v) ),
    file('ANA007-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Orderings_Oorder(u) ),
    file('ANA007-2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ c_lessequals(c_HOL_Oabs(v(v_x(u)),t_b),c_times(u,c_HOL_Oabs(v(v_x(u)),t_b),t_b),t_b),
    file('ANA007-2.p',unknown),
    [] ).

cnf(5,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('ANA007-2.p',unknown),
    [] ).

cnf(6,plain,
    equal(c_times(c_1,u,t_b),u),
    inference(res,[status(thm),theory(equality)],[5,2]),
    [iquote('0:Res:5.0,2.0')] ).

cnf(7,plain,
    class_Orderings_Oorder(t_b),
    inference(res,[status(thm),theory(equality)],[5,3]),
    [iquote('0:Res:5.0,3.0')] ).

cnf(11,plain,
    ~ c_lessequals(c_HOL_Oabs(v(v_x(c_1)),t_b),c_HOL_Oabs(v(v_x(c_1)),t_b),t_b),
    inference(spl,[status(thm),theory(equality)],[6,4]),
    [iquote('0:SpL:6.0,4.0')] ).

cnf(13,plain,
    ~ class_Orderings_Oorder(t_b),
    inference(res,[status(thm),theory(equality)],[1,11]),
    [iquote('0:Res:1.1,11.0')] ).

cnf(14,plain,
    $false,
    inference(ssi,[status(thm)],[13,5,7]),
    [iquote('0:SSi:13.0,5.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ANA007-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jul  8 06:58:44 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.41  
% 0.19/0.41  SPASS V 3.9 
% 0.19/0.41  SPASS beiseite: Proof found.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.19/0.41  SPASS allocated 75592 KBytes.
% 0.19/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.41  		0:00:00.04 for the input.
% 0.19/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41  		0:00:00.00 for inferences.
% 0.19/0.41  		0:00:00.00 for the backtracking.
% 0.19/0.41  		0:00:00.00 for the reduction.
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  Here is a proof with depth 3, length 10 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : cls_Orderings_Oorder__class_Oaxioms__1_0 cls_Ring__and__Field_Omult__cancel__right1_2 clsrel_Ring__and__Field_Oordered__idom_44 cls_conjecture_0 tfree_tcs
% 0.19/0.41  
%------------------------------------------------------------------------------