TSTP Solution File: ANA017-2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 19:28:45 EDT 2022

% Result   : Unsatisfiable 0.36s 0.54s
% Output   : Refutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   22 (  11 unt;   0 nHn;  22 RR)
%            Number of literals    :   38 (   0 equ;  22 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   8 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,c_HOL_Oabs(v,u),u) ),
    file('ANA017-2.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('ANA017-2.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('ANA017-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(u)
    | ~ c_lessequals(v,w,u)
    | ~ c_lessequals(c_0,x,u)
    | c_lessequals(c_times(x,v,u),c_times(x,w,u),u) ),
    file('ANA017-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Osemigroup__mult(u) ),
    file('ANA017-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Opordered__semiring(u) ),
    file('ANA017-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Olordered__ab__group__abs(u) ),
    file('ANA017-2.p',unknown),
    [] ).

cnf(8,axiom,
    c_lessequals(c_HOL_Oabs(v_b(u),t_b),c_times(v_ca,c_HOL_Oabs(v(u),t_b),t_b),t_b),
    file('ANA017-2.p',unknown),
    [] ).

cnf(9,axiom,
    ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(u)),t_b),t_b),c_times(u,c_HOL_Oabs(v(v_x(u)),t_b),t_b),t_b),
    file('ANA017-2.p',unknown),
    [] ).

cnf(10,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('ANA017-2.p',unknown),
    [] ).

cnf(11,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)],[10,3]),
    [iquote('0:Res:10.0,3.0')] ).

cnf(12,plain,
    class_OrderedGroup_Osemigroup__mult(t_b),
    inference(res,[status(thm),theory(equality)],[10,5]),
    [iquote('0:Res:10.0,5.0')] ).

cnf(13,plain,
    class_Ring__and__Field_Opordered__semiring(t_b),
    inference(res,[status(thm),theory(equality)],[10,6]),
    [iquote('0:Res:10.0,6.0')] ).

cnf(14,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(res,[status(thm),theory(equality)],[10,7]),
    [iquote('0:Res:10.0,7.0')] ).

cnf(29,plain,
    ( ~ class_OrderedGroup_Osemigroup__mult(t_b)
    | ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(u,v,t_b))),t_b),t_b),c_times(u,c_times(v,c_HOL_Oabs(v(v_x(c_times(u,v,t_b))),t_b),t_b),t_b),t_b) ),
    inference(spl,[status(thm),theory(equality)],[2,9]),
    [iquote('0:SpL:2.1,9.0')] ).

cnf(30,plain,
    ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(u,v,t_b))),t_b),t_b),c_times(u,c_times(v,c_HOL_Oabs(v(v_x(c_times(u,v,t_b))),t_b),t_b),t_b),t_b),
    inference(ssi,[status(thm)],[29,10,14,13,12]),
    [iquote('0:SSi:29.0,10.0,14.0,13.0,12.0')] ).

cnf(45,plain,
    ( ~ class_Ring__and__Field_Opordered__semiring(t_b)
    | ~ c_lessequals(c_HOL_Oabs(u,t_b),v,t_b)
    | ~ c_lessequals(c_0,c_HOL_Oabs(w,t_b),t_b)
    | c_lessequals(c_HOL_Oabs(c_times(w,u,t_b),t_b),c_times(c_HOL_Oabs(w,t_b),v,t_b),t_b) ),
    inference(spr,[status(thm),theory(equality)],[11,4]),
    [iquote('0:SpR:11.0,4.3')] ).

cnf(49,plain,
    ( ~ c_lessequals(c_HOL_Oabs(u,t_b),v,t_b)
    | ~ c_lessequals(c_0,c_HOL_Oabs(w,t_b),t_b)
    | c_lessequals(c_HOL_Oabs(c_times(w,u,t_b),t_b),c_times(c_HOL_Oabs(w,t_b),v,t_b),t_b) ),
    inference(ssi,[status(thm)],[45,10,14,13,12]),
    [iquote('0:SSi:45.0,10.0,14.0,13.0,12.0')] ).

cnf(255,plain,
    ( ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),u,t_b))),t_b),c_times(u,c_HOL_Oabs(v(v_x(c_times(c_HOL_Oabs(v_c,t_b),u,t_b))),t_b),t_b),t_b)
    | ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b) ),
    inference(res,[status(thm),theory(equality)],[49,30]),
    [iquote('0:Res:49.2,30.0')] ).

cnf(655,plain,
    ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b),
    inference(res,[status(thm),theory(equality)],[8,255]),
    [iquote('0:Res:8.0,255.0')] ).

cnf(656,plain,
    ~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(res,[status(thm),theory(equality)],[1,655]),
    [iquote('0:Res:1.1,655.0')] ).

cnf(657,plain,
    $false,
    inference(ssi,[status(thm)],[656,10,14,13,12]),
    [iquote('0:SSi:656.0,10.0,14.0,13.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n027.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 04:13:30 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.36/0.54  
% 0.36/0.54  SPASS V 3.9 
% 0.36/0.54  SPASS beiseite: Proof found.
% 0.36/0.54  % SZS status Theorem
% 0.36/0.54  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.36/0.54  SPASS derived 341 clauses, backtracked 0 clauses, performed 0 splits and kept 93 clauses.
% 0.36/0.54  SPASS allocated 76981 KBytes.
% 0.36/0.54  SPASS spent	0:00:00.18 on the problem.
% 0.36/0.54  		0:00:00.04 for the input.
% 0.36/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.54  		0:00:00.01 for inferences.
% 0.36/0.54  		0:00:00.00 for the backtracking.
% 0.36/0.54  		0:00:00.11 for the reduction.
% 0.36/0.54  
% 0.36/0.54  
% 0.36/0.54  Here is a proof with depth 5, length 22 :
% 0.36/0.54  % SZS output start Refutation
% See solution above
% 0.36/0.54  Formulae used in the proof : cls_OrderedGroup_Oabs__ge__zero_0 cls_OrderedGroup_Omult__ac__1_0 cls_Ring__and__Field_Oabs__mult_0 cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 clsrel_Ring__and__Field_Oordered__idom_21 clsrel_Ring__and__Field_Oordered__idom_42 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_1 tfree_tcs
% 0.36/0.54  
%------------------------------------------------------------------------------