TSTP Solution File: ALG219+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG219+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 18:03:02 EDT 2022

% Result   : Theorem 6.53s 6.73s
% Output   : Refutation 6.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   34
% Syntax   : Number of clauses     :   56 (  27 unt;  21 nHn;  56 RR)
%            Number of literals    :  428 (   0 equ; 328 neg)
%            Maximal clause size   :   31 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   26 (  25 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   6 con; 0-5 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    v3_rlvect_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(2,axiom,
    v4_rlvect_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(3,axiom,
    v5_rlvect_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(4,axiom,
    v6_rlvect_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(5,axiom,
    v4_group_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(6,axiom,
    v7_group_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(7,axiom,
    v6_vectsp_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(8,axiom,
    v7_vectsp_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(9,axiom,
    v8_vectsp_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(10,axiom,
    v2_vectsp_2(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(11,axiom,
    l3_vectsp_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(12,axiom,
    v3_rlvect_1(skc14),
    file('ALG219+1.p',unknown),
    [] ).

cnf(13,axiom,
    v4_rlvect_1(skc14),
    file('ALG219+1.p',unknown),
    [] ).

cnf(14,axiom,
    v5_rlvect_1(skc14),
    file('ALG219+1.p',unknown),
    [] ).

cnf(15,axiom,
    v6_rlvect_1(skc14),
    file('ALG219+1.p',unknown),
    [] ).

cnf(27,axiom,
    ~ v3_struct_0(skc14),
    file('ALG219+1.p',unknown),
    [] ).

cnf(28,axiom,
    ~ v3_struct_0(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(29,axiom,
    ~ v10_vectsp_1(skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(30,axiom,
    v3_vectsp_2(skc14,skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(31,axiom,
    v5_vectsp_2(skc14,skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(32,axiom,
    l1_vectsp_2(skc14,skc13),
    file('ALG219+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ l2_struct_0(u)
    | l1_struct_0(u) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ l2_vectsp_1(u)
    | l1_vectsp_1(u) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ l2_vectsp_1(u)
    | l2_struct_0(u) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ l3_vectsp_1(u)
    | l2_vectsp_1(u) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(54,axiom,
    m1_subset_1(u1_struct_0(skc14),k1_zfmisc_1(u1_struct_0(skc14))),
    file('ALG219+1.p',unknown),
    [] ).

cnf(55,axiom,
    ~ equal(k2_group_1(skc13),k1_rlvect_1(skc13)),
    file('ALG219+1.p',unknown),
    [] ).

cnf(68,axiom,
    ~ equal(k1_rmod_5(skc13,skc14,u1_struct_0(skc14)),skc14),
    file('ALG219+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ l1_struct_0(u)
    | ~ l1_vectsp_2(v,u)
    | l1_rlvect_1(v) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ v6_vectsp_1(u)
    | ~ v7_group_1(u)
    | ~ l1_vectsp_1(u)
    | v3_struct_0(u)
    | v2_group_1(u) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(96,axiom,
    ( ~ l1_struct_0(u)
    | ~ l1_vectsp_2(v,u)
    | ~ v3_vectsp_2(v,u)
    | equal(g1_vectsp_2(u,u1_struct_0(v),u1_rlvect_1(v),u2_struct_0(v),u1_vectsp_2(u,v)),v) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(123,axiom,
    ( ~ v3_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v6_rlvect_1(u)
    | ~ l3_vectsp_1(v)
    | ~ v8_vectsp_1(v)
    | ~ v7_vectsp_1(v)
    | ~ v6_vectsp_1(v)
    | ~ v4_group_1(v)
    | ~ v6_rlvect_1(v)
    | ~ v5_rlvect_1(v)
    | ~ v4_rlvect_1(v)
    | ~ v3_rlvect_1(v)
    | ~ l1_vectsp_2(u,v)
    | ~ v5_vectsp_2(u,v)
    | v3_struct_0(u)
    | v3_struct_0(v)
    | m1_rmod_2(k2_rmod_2(v,u),v,u) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(136,axiom,
    ( ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ l3_vectsp_1(v)
    | ~ v8_vectsp_1(v)
    | ~ v7_vectsp_1(v)
    | ~ v6_vectsp_1(v)
    | ~ v4_group_1(v)
    | ~ v6_rlvect_1(v)
    | ~ v5_rlvect_1(v)
    | ~ v4_rlvect_1(v)
    | ~ v3_rlvect_1(v)
    | ~ l1_vectsp_2(u,v)
    | ~ v5_vectsp_2(u,v)
    | v3_struct_0(u)
    | v3_struct_0(v)
    | equal(g1_vectsp_2(v,u1_struct_0(u),u1_rlvect_1(u),u2_struct_0(u),u1_vectsp_2(v,u)),k2_rmod_2(v,u)) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(139,axiom,
    ( ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ l3_vectsp_1(v)
    | ~ v2_vectsp_2(v)
    | ~ v8_vectsp_1(v)
    | ~ v7_vectsp_1(v)
    | ~ v6_vectsp_1(v)
    | ~ v7_group_1(v)
    | ~ v4_group_1(v)
    | ~ v6_rlvect_1(v)
    | ~ v5_rlvect_1(v)
    | ~ v4_rlvect_1(v)
    | ~ v3_rlvect_1(v)
    | ~ v3_vectsp_2(w,v)
    | ~ l1_vectsp_2(u,v)
    | ~ v5_vectsp_2(u,v)
    | ~ equal(x,u1_struct_0(w))
    | ~ m1_subset_1(x,k1_zfmisc_1(u1_struct_0(u)))
    | ~ m1_rmod_2(w,v,u)
    | v3_struct_0(u)
    | v10_vectsp_1(v)
    | v3_struct_0(v)
    | equal(k2_group_1(v),k1_rlvect_1(v))
    | equal(k1_rmod_5(v,u,x),w) ),
    file('ALG219+1.p',unknown),
    [] ).

cnf(294,plain,
    ( ~ v3_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v4_group_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v8_vectsp_1(u)
    | ~ l3_vectsp_1(u)
    | ~ v6_rlvect_1(skc14)
    | ~ v5_rlvect_1(skc14)
    | ~ v3_rlvect_1(skc14)
    | ~ v5_vectsp_2(skc14,u)
    | ~ l1_vectsp_2(skc14,u)
    | m1_rmod_2(k2_rmod_2(u,skc14),u,skc14)
    | v3_struct_0(u)
    | v3_struct_0(skc14) ),
    inference(res,[status(thm),theory(equality)],[13,123]),
    [iquote('0:Res:13.0,123.11')] ).

cnf(334,plain,
    ( ~ l3_vectsp_1(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | v3_struct_0(u)
    | m1_rmod_2(k2_rmod_2(u,skc14),u,skc14) ),
    inference(mrr,[status(thm)],[294,15,14,12,27]),
    [iquote('0:MRR:294.9,294.10,294.11,294.16,15.0,14.0,12.0,27.0')] ).

cnf(375,plain,
    ( ~ l1_struct_0(skc13)
    | l1_rlvect_1(skc14) ),
    inference(res,[status(thm),theory(equality)],[32,75]),
    [iquote('0:Res:32.0,75.1')] ).

cnf(379,plain,
    l1_rlvect_1(skc14),
    inference(ssi,[status(thm)],[375,50,48,46,10,6,8,5,11,9,7,4,3,2,1]),
    [iquote('0:SSi:375.0,50.0,48.0,46.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.1,2.1,1.1')] ).

cnf(446,plain,
    ( ~ v6_vectsp_1(skc13)
    | ~ v7_group_1(skc13)
    | ~ l1_vectsp_1(skc13)
    | v2_group_1(skc13) ),
    inference(res,[status(thm),theory(equality)],[90,28]),
    [iquote('0:Res:90.3,28.0')] ).

cnf(452,plain,
    v2_group_1(skc13),
    inference(ssi,[status(thm)],[446,50,47,10,6,8,5,11,9,7,4,3,2,1]),
    [iquote('0:SSi:446.2,446.1,446.0,50.0,47.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.1,1.1')] ).

cnf(1238,plain,
    ( ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ l3_vectsp_1(v)
    | ~ v8_vectsp_1(v)
    | ~ v7_vectsp_1(v)
    | ~ v6_vectsp_1(v)
    | ~ v4_group_1(v)
    | ~ v6_rlvect_1(v)
    | ~ v5_rlvect_1(v)
    | ~ v4_rlvect_1(v)
    | ~ v3_rlvect_1(v)
    | ~ l1_struct_0(v)
    | ~ l1_vectsp_2(u,v)
    | ~ v5_vectsp_2(u,v)
    | ~ l1_vectsp_2(u,v)
    | ~ v3_vectsp_2(u,v)
    | v3_struct_0(u)
    | v3_struct_0(v)
    | equal(k2_rmod_2(v,u),u) ),
    inference(spr,[status(thm),theory(equality)],[136,96]),
    [iquote('0:SpR:136.17,96.3')] ).

cnf(1251,plain,
    ( ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ l3_vectsp_1(v)
    | ~ v8_vectsp_1(v)
    | ~ v7_vectsp_1(v)
    | ~ v6_vectsp_1(v)
    | ~ v4_group_1(v)
    | ~ v6_rlvect_1(v)
    | ~ v5_rlvect_1(v)
    | ~ v4_rlvect_1(v)
    | ~ v3_rlvect_1(v)
    | ~ l1_struct_0(v)
    | ~ v5_vectsp_2(u,v)
    | ~ l1_vectsp_2(u,v)
    | ~ v3_vectsp_2(u,v)
    | v3_struct_0(u)
    | v3_struct_0(v)
    | equal(k2_rmod_2(v,u),u) ),
    inference(obv,[status(thm),theory(equality)],[1238]),
    [iquote('0:Obv:1238.14')] ).

cnf(1252,plain,
    ( ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ l3_vectsp_1(v)
    | ~ v8_vectsp_1(v)
    | ~ v7_vectsp_1(v)
    | ~ v6_vectsp_1(v)
    | ~ v4_group_1(v)
    | ~ v6_rlvect_1(v)
    | ~ v5_rlvect_1(v)
    | ~ v4_rlvect_1(v)
    | ~ v3_rlvect_1(v)
    | ~ v5_vectsp_2(u,v)
    | ~ l1_vectsp_2(u,v)
    | ~ v3_vectsp_2(u,v)
    | v3_struct_0(u)
    | v3_struct_0(v)
    | equal(k2_rmod_2(v,u),u) ),
    inference(ssi,[status(thm)],[1251,50,48,46]),
    [iquote('0:SSi:1251.13,50.1,48.1,46.1')] ).

cnf(1317,plain,
    ( ~ v6_rlvect_1(skc14)
    | ~ v5_rlvect_1(skc14)
    | ~ v4_rlvect_1(skc14)
    | ~ v3_rlvect_1(skc14)
    | ~ l3_vectsp_1(u)
    | ~ v2_vectsp_2(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v7_group_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v3_vectsp_2(v,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | ~ equal(u1_struct_0(skc14),u1_struct_0(v))
    | ~ m1_rmod_2(v,u,skc14)
    | v3_struct_0(skc14)
    | v10_vectsp_1(u)
    | v3_struct_0(u)
    | equal(k2_group_1(u),k1_rlvect_1(u))
    | equal(k1_rmod_5(u,skc14,u1_struct_0(skc14)),v) ),
    inference(res,[status(thm),theory(equality)],[54,139]),
    [iquote('0:Res:54.0,139.19')] ).

cnf(1320,plain,
    ( ~ l3_vectsp_1(u)
    | ~ v2_vectsp_2(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v7_group_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v3_vectsp_2(v,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | ~ equal(u1_struct_0(skc14),u1_struct_0(v))
    | ~ m1_rmod_2(v,u,skc14)
    | v3_struct_0(skc14)
    | v10_vectsp_1(u)
    | v3_struct_0(u)
    | equal(k2_group_1(u),k1_rlvect_1(u))
    | equal(k1_rmod_5(u,skc14,u1_struct_0(skc14)),v) ),
    inference(ssi,[status(thm)],[1317,15,14,13,12,379]),
    [iquote('0:SSi:1317.3,1317.2,1317.1,1317.0,15.0,14.0,13.0,12.0,379.0,15.0,14.0,13.0,12.0,379.0,15.0,14.0,13.0,12.0,379.0,15.0,14.0,13.0,12.0,379.0')] ).

cnf(1321,plain,
    ( ~ l3_vectsp_1(u)
    | ~ v2_vectsp_2(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v7_group_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v3_vectsp_2(v,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | ~ equal(u1_struct_0(skc14),u1_struct_0(v))
    | ~ m1_rmod_2(v,u,skc14)
    | v10_vectsp_1(u)
    | v3_struct_0(u)
    | equal(k2_group_1(u),k1_rlvect_1(u))
    | equal(k1_rmod_5(u,skc14,u1_struct_0(skc14)),v) ),
    inference(mrr,[status(thm)],[1320,27]),
    [iquote('0:MRR:1320.16,27.0')] ).

cnf(2954,plain,
    ( ~ v6_rlvect_1(skc14)
    | ~ v5_rlvect_1(skc14)
    | ~ v4_rlvect_1(skc14)
    | ~ v3_rlvect_1(skc14)
    | ~ l3_vectsp_1(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ l3_vectsp_1(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v5_vectsp_2(skc14,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v3_vectsp_2(skc14,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | v3_struct_0(skc14)
    | v3_struct_0(u)
    | v3_struct_0(u)
    | m1_rmod_2(skc14,u,skc14) ),
    inference(spr,[status(thm),theory(equality)],[1252,334]),
    [iquote('0:SpR:1252.18,334.12')] ).

cnf(2955,plain,
    ( ~ v6_rlvect_1(skc14)
    | ~ v5_rlvect_1(skc14)
    | ~ v4_rlvect_1(skc14)
    | ~ v3_rlvect_1(skc14)
    | ~ l3_vectsp_1(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v3_vectsp_2(skc14,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | v3_struct_0(skc14)
    | v3_struct_0(u)
    | m1_rmod_2(skc14,u,skc14) ),
    inference(obv,[status(thm),theory(equality)],[2954]),
    [iquote('0:Obv:2954.28')] ).

cnf(2956,plain,
    ( ~ l3_vectsp_1(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v3_vectsp_2(skc14,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | v3_struct_0(skc14)
    | v3_struct_0(u)
    | m1_rmod_2(skc14,u,skc14) ),
    inference(ssi,[status(thm)],[2955,15,14,13,12,379]),
    [iquote('0:SSi:2955.3,2955.2,2955.1,2955.0,15.0,14.0,13.0,12.0,379.0,15.0,14.0,13.0,12.0,379.0,15.0,14.0,13.0,12.0,379.0,15.0,14.0,13.0,12.0,379.0')] ).

cnf(2957,plain,
    ( ~ l3_vectsp_1(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v3_vectsp_2(skc14,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | v3_struct_0(u)
    | m1_rmod_2(skc14,u,skc14) ),
    inference(mrr,[status(thm)],[2956,27]),
    [iquote('0:MRR:2956.12,27.0')] ).

cnf(3701,plain,
    ( ~ l3_vectsp_1(u)
    | ~ v2_vectsp_2(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v7_group_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v3_vectsp_2(skc14,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | ~ m1_rmod_2(skc14,u,skc14)
    | v10_vectsp_1(u)
    | v3_struct_0(u)
    | equal(k2_group_1(u),k1_rlvect_1(u))
    | equal(k1_rmod_5(u,skc14,u1_struct_0(skc14)),skc14) ),
    inference(eqr,[status(thm),theory(equality)],[1321]),
    [iquote('0:EqR:1321.14')] ).

cnf(3702,plain,
    ( ~ l3_vectsp_1(u)
    | ~ v2_vectsp_2(u)
    | ~ v8_vectsp_1(u)
    | ~ v7_vectsp_1(u)
    | ~ v6_vectsp_1(u)
    | ~ v7_group_1(u)
    | ~ v4_group_1(u)
    | ~ v6_rlvect_1(u)
    | ~ v5_rlvect_1(u)
    | ~ v4_rlvect_1(u)
    | ~ v3_rlvect_1(u)
    | ~ v3_vectsp_2(skc14,u)
    | ~ l1_vectsp_2(skc14,u)
    | ~ v5_vectsp_2(skc14,u)
    | v10_vectsp_1(u)
    | v3_struct_0(u)
    | equal(k2_group_1(u),k1_rlvect_1(u))
    | equal(k1_rmod_5(u,skc14,u1_struct_0(skc14)),skc14) ),
    inference(mrr,[status(thm)],[3701,2957]),
    [iquote('0:MRR:3701.14,2957.13')] ).

cnf(5752,plain,
    ( ~ l3_vectsp_1(skc13)
    | ~ v2_vectsp_2(skc13)
    | ~ v8_vectsp_1(skc13)
    | ~ v7_vectsp_1(skc13)
    | ~ v6_vectsp_1(skc13)
    | ~ v7_group_1(skc13)
    | ~ v4_group_1(skc13)
    | ~ v6_rlvect_1(skc13)
    | ~ v5_rlvect_1(skc13)
    | ~ v4_rlvect_1(skc13)
    | ~ v3_rlvect_1(skc13)
    | ~ v3_vectsp_2(skc14,skc13)
    | ~ l1_vectsp_2(skc14,skc13)
    | ~ v5_vectsp_2(skc14,skc13)
    | ~ equal(skc14,skc14)
    | v10_vectsp_1(skc13)
    | v3_struct_0(skc13)
    | equal(k2_group_1(skc13),k1_rlvect_1(skc13)) ),
    inference(spl,[status(thm),theory(equality)],[3702,68]),
    [iquote('0:SpL:3702.17,68.0')] ).

cnf(5753,plain,
    ( ~ l3_vectsp_1(skc13)
    | ~ v2_vectsp_2(skc13)
    | ~ v8_vectsp_1(skc13)
    | ~ v7_vectsp_1(skc13)
    | ~ v6_vectsp_1(skc13)
    | ~ v7_group_1(skc13)
    | ~ v4_group_1(skc13)
    | ~ v6_rlvect_1(skc13)
    | ~ v5_rlvect_1(skc13)
    | ~ v4_rlvect_1(skc13)
    | ~ v3_rlvect_1(skc13)
    | ~ v3_vectsp_2(skc14,skc13)
    | ~ l1_vectsp_2(skc14,skc13)
    | ~ v5_vectsp_2(skc14,skc13)
    | v10_vectsp_1(skc13)
    | v3_struct_0(skc13)
    | equal(k2_group_1(skc13),k1_rlvect_1(skc13)) ),
    inference(obv,[status(thm),theory(equality)],[5752]),
    [iquote('0:Obv:5752.14')] ).

cnf(5754,plain,
    ( ~ v3_vectsp_2(skc14,skc13)
    | ~ l1_vectsp_2(skc14,skc13)
    | ~ v5_vectsp_2(skc14,skc13)
    | v10_vectsp_1(skc13)
    | v3_struct_0(skc13)
    | equal(k2_group_1(skc13),k1_rlvect_1(skc13)) ),
    inference(ssi,[status(thm)],[5753,10,6,8,5,11,9,7,4,3,2,1,452]),
    [iquote('0:SSi:5753.10,5753.9,5753.8,5753.7,5753.6,5753.5,5753.4,5753.3,5753.2,5753.1,5753.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,452.0')] ).

cnf(5755,plain,
    $false,
    inference(mrr,[status(thm)],[5754,30,32,31,29,28,55]),
    [iquote('0:MRR:5754.0,5754.1,5754.2,5754.3,5754.4,5754.5,30.0,32.0,31.0,29.0,28.0,55.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : ALG219+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n024.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 : Wed Jun  8 02:01:34 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 6.53/6.73  
% 6.53/6.73  SPASS V 3.9 
% 6.53/6.73  SPASS beiseite: Proof found.
% 6.53/6.73  % SZS status Theorem
% 6.53/6.73  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 6.53/6.73  SPASS derived 4589 clauses, backtracked 0 clauses, performed 0 splits and kept 3385 clauses.
% 6.53/6.73  SPASS allocated 107594 KBytes.
% 6.53/6.73  SPASS spent	0:00:06.39 on the problem.
% 6.53/6.73  		0:00:00.03 for the input.
% 6.53/6.73  		0:00:00.11 for the FLOTTER CNF translation.
% 6.53/6.73  		0:00:00.16 for inferences.
% 6.53/6.73  		0:00:00.00 for the backtracking.
% 6.53/6.73  		0:00:05.90 for the reduction.
% 6.53/6.73  
% 6.53/6.73  
% 6.53/6.73  Here is a proof with depth 3, length 56 :
% 6.53/6.73  % SZS output start Refutation
% See solution above
% 6.61/6.87  Formulae used in the proof : t14_rmod_5 dt_l2_struct_0 dt_l2_vectsp_1 dt_l3_vectsp_1 dt_l1_vectsp_2 cc3_vectsp_2 abstractness_v3_vectsp_2 dt_k2_rmod_2 d4_rmod_2 t13_rmod_5
% 6.61/6.87  
%------------------------------------------------------------------------------