TSTP Solution File: ANA030-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 19:28:54 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   33 (  11 unt;   0 nHn;  33 RR)
%            Number of literals    :   61 (   0 equ;  29 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 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('ANA030-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_plus(v,c_uminus(w,u),u),c_minus(v,w,u)) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(u)
    | ~ c_lessequals(c_minus(v,w,u),x,u)
    | c_lessequals(v,c_plus(x,w,u),u) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_minus(v,c_uminus(w,u),u),c_plus(v,w,u)) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_plus(c_uminus(v,u),c_uminus(w,u),u),c_uminus(c_plus(v,w,u),u)) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_uminus(c_minus(v,w,u),u),c_minus(w,v,u)) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_uminus(c_uminus(v,u),u),v) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ class_Orderings_Olinorder(u)
    | c_lessequals(v,c_Orderings_Omax(w,v,u),u) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ class_Orderings_Olinorder(u)
    | ~ c_lessequals(c_Orderings_Omax(v,w,u),x,u)
    | c_lessequals(v,x,u) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
    | class_OrderedGroup_Opordered__ab__group__add(u) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Orderings_Olinorder(u) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Oab__group__add(u) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Olordered__ab__group__abs(u) ),
    file('ANA030-2.p',unknown),
    [] ).

cnf(14,axiom,
    c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v(u),v_g(u),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),
    file('ANA030-2.p',unknown),
    [] ).

cnf(15,axiom,
    ~ c_lessequals(v(v_x(u)),c_plus(v_g(v_x(u)),c_times(u,c_HOL_Oabs(v_h(v_x(u)),t_b),t_b),t_b),t_b),
    file('ANA030-2.p',unknown),
    [] ).

cnf(16,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('ANA030-2.p',unknown),
    [] ).

cnf(17,plain,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_minus(c_uminus(v,u),w,u),c_uminus(c_plus(v,w,u),u)) ),
    inference(rew,[status(thm),theory(equality)],[2,5]),
    [iquote('0:Rew:2.1,5.1')] ).

cnf(18,plain,
    class_Orderings_Olinorder(t_b),
    inference(res,[status(thm),theory(equality)],[16,11]),
    [iquote('0:Res:16.0,11.0')] ).

cnf(19,plain,
    class_OrderedGroup_Oab__group__add(t_b),
    inference(res,[status(thm),theory(equality)],[16,12]),
    [iquote('0:Res:16.0,12.0')] ).

cnf(20,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(res,[status(thm),theory(equality)],[16,13]),
    [iquote('0:Res:16.0,13.0')] ).

cnf(26,plain,
    ( ~ class_Orderings_Olinorder(u)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(u)
    | equal(c_HOL_Oabs(c_Orderings_Omax(v,c_0,u),u),c_Orderings_Omax(v,c_0,u)) ),
    inference(res,[status(thm),theory(equality)],[8,1]),
    [iquote('0:Res:8.1,1.1')] ).

cnf(49,plain,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_uminus(c_uminus(c_plus(v,w,u),u),u),c_minus(w,c_uminus(v,u),u)) ),
    inference(spr,[status(thm),theory(equality)],[17,6]),
    [iquote('0:SpR:17.1,6.1')] ).

cnf(54,plain,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_uminus(c_uminus(c_plus(v,w,u),u),u),c_minus(w,c_uminus(v,u),u)) ),
    inference(obv,[status(thm),theory(equality)],[49]),
    [iquote('0:Obv:49.0')] ).

cnf(55,plain,
    ( ~ class_OrderedGroup_Oab__group__add(u)
    | equal(c_plus(v,w,u),c_plus(w,v,u)) ),
    inference(rew,[status(thm),theory(equality)],[7,54,4]),
    [iquote('0:Rew:7.1,54.1,4.1,54.1')] ).

cnf(426,plain,
    ( ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | c_lessequals(c_Orderings_Omax(c_minus(v(u),v_g(u),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b) ),
    inference(spr,[status(thm),theory(equality)],[26,14]),
    [iquote('0:SpR:26.2,14.0')] ).

cnf(427,plain,
    c_lessequals(c_Orderings_Omax(c_minus(v(u),v_g(u),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),
    inference(ssi,[status(thm)],[426,16,20,18,19]),
    [iquote('0:SSi:426.1,426.0,16.0,20.0,18.0,19.0,16.0,20.0,18.0,19.0')] ).

cnf(428,plain,
    ( ~ class_Orderings_Olinorder(t_b)
    | c_lessequals(c_minus(v(u),v_g(u),t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b) ),
    inference(res,[status(thm),theory(equality)],[427,9]),
    [iquote('0:Res:427.0,9.1')] ).

cnf(429,plain,
    c_lessequals(c_minus(v(u),v_g(u),t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),
    inference(ssi,[status(thm)],[428,16,20,18,19]),
    [iquote('0:SSi:428.0,16.0,20.0,18.0,19.0')] ).

cnf(430,plain,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
    | c_lessequals(v(u),c_plus(c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),v_g(u),t_b),t_b) ),
    inference(res,[status(thm),theory(equality)],[429,3]),
    [iquote('0:Res:429.0,3.1')] ).

cnf(431,plain,
    c_lessequals(v(u),c_plus(c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),v_g(u),t_b),t_b),
    inference(ssi,[status(thm)],[430,10,16,20,18,19]),
    [iquote('0:SSi:430.0,10.0,16.0,20.0,18.0,19.1')] ).

cnf(432,plain,
    ( ~ class_OrderedGroup_Oab__group__add(t_b)
    | c_lessequals(v(u),c_plus(v_g(u),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),t_b) ),
    inference(spr,[status(thm),theory(equality)],[55,431]),
    [iquote('0:SpR:55.1,431.0')] ).

cnf(434,plain,
    c_lessequals(v(u),c_plus(v_g(u),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),t_b),
    inference(ssi,[status(thm)],[432,16,20,18,19]),
    [iquote('0:SSi:432.0,16.0,20.0,18.0,19.0')] ).

cnf(435,plain,
    $false,
    inference(unc,[status(thm)],[434,15]),
    [iquote('0:UnC:434.0,15.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  8 05:53:36 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 201 clauses, backtracked 0 clauses, performed 0 splits and kept 67 clauses.
% 0.20/0.44  SPASS allocated 76060 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.44  		0:00:00.04 for the input.
% 0.20/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.01 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.02 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 5, length 33 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : cls_OrderedGroup_Oabs__of__nonneg_0 cls_OrderedGroup_Ocompare__rls__1_0 cls_OrderedGroup_Ocompare__rls__8_0 cls_OrderedGroup_Odiff__minus__eq__add_0 cls_OrderedGroup_Ominus__add__distrib_0 cls_OrderedGroup_Ominus__diff__eq_0 cls_OrderedGroup_Ominus__minus_0 cls_Orderings_Ole__maxI2_0 cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0 clsrel_OrderedGroup_Olordered__ab__group__abs_1 clsrel_Ring__and__Field_Oordered__idom_33 clsrel_Ring__and__Field_Oordered__idom_4 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_1 cls_conjecture_2 tfree_tcs
% 0.20/0.44  
%------------------------------------------------------------------------------