TSTP Solution File: ANA010-2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 19:28:40 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   20 (  11 unt;   0 nHn;  20 RR)
%            Number of literals    :   33 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
    | ~ c_lessequals(c_0,v,u)
    | equal(c_HOL_Oabs(v,u),v) ),
    file('ANA010-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ class_Orderings_Oorder(u)
    | ~ c_lessequals(v,w,u)
    | ~ c_lessequals(w,x,u)
    | c_lessequals(v,x,u) ),
    file('ANA010-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | equal(c_times(c_HOL_Oabs(v,u),c_HOL_Oabs(w,u),u),c_HOL_Oabs(c_times(v,w,u),u)) ),
    file('ANA010-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
    | class_Orderings_Oorder(u) ),
    file('ANA010-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Olordered__ab__group__abs(u) ),
    file('ANA010-2.p',unknown),
    [] ).

cnf(6,axiom,
    c_lessequals(c_0,v(u),t_b),
    file('ANA010-2.p',unknown),
    [] ).

cnf(7,axiom,
    c_lessequals(v(u),c_times(v_c,v_g(u),t_b),t_b),
    file('ANA010-2.p',unknown),
    [] ).

cnf(8,axiom,
    ~ c_lessequals(v(v_x(u)),c_times(u,c_HOL_Oabs(v_g(v_x(u)),t_b),t_b),t_b),
    file('ANA010-2.p',unknown),
    [] ).

cnf(9,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('ANA010-2.p',unknown),
    [] ).

cnf(10,plain,
    equal(c_times(c_HOL_Oabs(u,t_b),c_HOL_Oabs(v,t_b),t_b),c_HOL_Oabs(c_times(u,v,t_b),t_b)),
    inference(res,[status(thm),theory(equality)],[9,3]),
    [iquote('0:Res:9.0,3.0')] ).

cnf(11,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(res,[status(thm),theory(equality)],[9,5]),
    [iquote('0:Res:9.0,5.0')] ).

cnf(16,plain,
    ( ~ class_Orderings_Oorder(t_b)
    | ~ c_lessequals(u,v(v),t_b)
    | c_lessequals(u,c_times(v_c,v_g(v),t_b),t_b) ),
    inference(res,[status(thm),theory(equality)],[7,2]),
    [iquote('0:Res:7.0,2.1')] ).

cnf(18,plain,
    ( ~ class_Orderings_Oorder(t_b)
    | c_lessequals(c_0,c_times(v_c,v_g(u),t_b),t_b) ),
    inference(res,[status(thm),theory(equality)],[6,16]),
    [iquote('0:Res:6.0,16.1')] ).

cnf(21,plain,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | c_lessequals(c_0,c_times(v_c,v_g(u),t_b),t_b) ),
    inference(sor,[status(thm)],[18,4]),
    [iquote('0:SoR:18.0,4.1')] ).

cnf(22,plain,
    c_lessequals(c_0,c_times(v_c,v_g(u),t_b),t_b),
    inference(ssi,[status(thm)],[21,9,11]),
    [iquote('0:SSi:21.0,9.0,11.0')] ).

cnf(26,plain,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | equal(c_HOL_Oabs(c_times(v_c,v_g(u),t_b),t_b),c_times(v_c,v_g(u),t_b)) ),
    inference(res,[status(thm),theory(equality)],[22,1]),
    [iquote('0:Res:22.0,1.1')] ).

cnf(28,plain,
    equal(c_HOL_Oabs(c_times(v_c,v_g(u),t_b),t_b),c_times(v_c,v_g(u),t_b)),
    inference(ssi,[status(thm)],[26,9,11]),
    [iquote('0:SSi:26.0,9.0,11.0')] ).

cnf(41,plain,
    ~ c_lessequals(v(v_x(c_HOL_Oabs(u,t_b))),c_HOL_Oabs(c_times(u,v_g(v_x(c_HOL_Oabs(u,t_b))),t_b),t_b),t_b),
    inference(spl,[status(thm),theory(equality)],[10,8]),
    [iquote('0:SpL:10.0,8.0')] ).

cnf(94,plain,
    ~ c_lessequals(v(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),
    inference(spl,[status(thm),theory(equality)],[28,41]),
    [iquote('0:SpL:28.0,41.0')] ).

cnf(98,plain,
    $false,
    inference(mrr,[status(thm)],[94,7]),
    [iquote('0:MRR:94.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n011.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 03:47:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.42  
% 0.20/0.42  SPASS V 3.9 
% 0.20/0.42  SPASS beiseite: Proof found.
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.42  SPASS derived 76 clauses, backtracked 0 clauses, performed 0 splits and kept 49 clauses.
% 0.20/0.42  SPASS allocated 75746 KBytes.
% 0.20/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.42  		0:00:00.04 for the input.
% 0.20/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42  		0:00:00.00 for inferences.
% 0.20/0.42  		0:00:00.00 for the backtracking.
% 0.20/0.42  		0:00:00.01 for the reduction.
% 0.20/0.42  
% 0.20/0.42  
% 0.20/0.42  Here is a proof with depth 5, length 20 :
% 0.20/0.42  % SZS output start Refutation
% See solution above
% 0.20/0.42  Formulae used in the proof : cls_OrderedGroup_Oabs__of__nonneg_0 cls_Orderings_Oorder__class_Oorder__trans_0 cls_Ring__and__Field_Oabs__mult_0 clsrel_OrderedGroup_Olordered__ab__group__abs_17 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 tfree_tcs
% 0.20/0.42  
%------------------------------------------------------------------------------