TSTP Solution File: ANA016-2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ANA016-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 19:28:44 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   18 (   7 unt;   3 nHn;  18 RR)
%            Number of literals    :   34 (   0 equ;  18 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(u)
    | equal(c_times(c_1,v,u),v) ),
    file('ANA016-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ class_OrderedGroup_Osemigroup__mult(u)
    | equal(c_times(c_times(v,w,u),x,u),c_times(v,c_times(w,x,u),u)) ),
    file('ANA016-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ class_Ring__and__Field_Ofield(u)
    | equal(v,c_0)
    | equal(c_times(v,c_HOL_Oinverse(v,u),u),c_1) ),
    file('ANA016-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ class_Ring__and__Field_Ofield(u)
    | class_OrderedGroup_Omonoid__mult(u) ),
    file('ANA016-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ class_Ring__and__Field_Ofield(u)
    | class_OrderedGroup_Osemigroup__mult(u) ),
    file('ANA016-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(u)
    | class_Ring__and__Field_Ofield(u) ),
    file('ANA016-2.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(c_0,v_c),
    file('ANA016-2.p',unknown),
    [] ).

cnf(8,axiom,
    ~ equal(c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),v_g(v_x)),
    file('ANA016-2.p',unknown),
    [] ).

cnf(9,axiom,
    class_Ring__and__Field_Oordered__field(t_a),
    file('ANA016-2.p',unknown),
    [] ).

cnf(10,plain,
    class_Ring__and__Field_Ofield(t_a),
    inference(res,[status(thm),theory(equality)],[9,6]),
    [iquote('0:Res:9.0,6.0')] ).

cnf(69,plain,
    ( ~ class_Ring__and__Field_Ofield(u)
    | ~ class_OrderedGroup_Osemigroup__mult(u)
    | equal(v,c_0)
    | equal(c_times(v,c_times(c_HOL_Oinverse(v,u),w,u),u),c_times(c_1,w,u)) ),
    inference(spr,[status(thm),theory(equality)],[3,2]),
    [iquote('0:SpR:3.2,2.1')] ).

cnf(75,plain,
    ( ~ class_Ring__and__Field_Ofield(u)
    | equal(v,c_0)
    | equal(c_times(v,c_times(c_HOL_Oinverse(v,u),w,u),u),c_times(c_1,w,u)) ),
    inference(ssi,[status(thm)],[69,5]),
    [iquote('0:SSi:69.1,5.1')] ).

cnf(84,plain,
    ( ~ class_Ring__and__Field_Ofield(t_a)
    | ~ equal(c_times(c_1,v_g(v_x),t_a),v_g(v_x))
    | equal(c_0,v_c) ),
    inference(spl,[status(thm),theory(equality)],[75,8]),
    [iquote('0:SpL:75.2,8.0')] ).

cnf(85,plain,
    ( ~ equal(c_times(c_1,v_g(v_x),t_a),v_g(v_x))
    | equal(c_0,v_c) ),
    inference(ssi,[status(thm)],[84,9,10]),
    [iquote('0:SSi:84.0,9.0,10.0')] ).

cnf(86,plain,
    ~ equal(c_times(c_1,v_g(v_x),t_a),v_g(v_x)),
    inference(mrr,[status(thm)],[85,7]),
    [iquote('0:MRR:85.1,7.0')] ).

cnf(93,plain,
    ( ~ class_OrderedGroup_Omonoid__mult(t_a)
    | ~ equal(v_g(v_x),v_g(v_x)) ),
    inference(spl,[status(thm),theory(equality)],[1,86]),
    [iquote('0:SpL:1.1,86.0')] ).

cnf(94,plain,
    ~ class_OrderedGroup_Omonoid__mult(t_a),
    inference(obv,[status(thm),theory(equality)],[93]),
    [iquote('0:Obv:93.1')] ).

cnf(95,plain,
    $false,
    inference(ssi,[status(thm)],[94,4,9,10]),
    [iquote('0:SSi:94.0,4.0,9.0,10.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ANA016-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n009.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 : Fri Jul  8 02:41:37 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 57 clauses, backtracked 6 clauses, performed 2 splits and kept 40 clauses.
% 0.19/0.42  SPASS allocated 75709 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 3, length 18 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0 cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0 cls_Ring__and__Field_Oright__inverse_0 clsrel_Ring__and__Field_Ofield_12 clsrel_Ring__and__Field_Ofield_21 clsrel_Ring__and__Field_Oordered__field_0 cls_conjecture_0 cls_conjecture_2 tfree_tcs
% 0.19/0.42  
%------------------------------------------------------------------------------