TSTP Solution File: RNG082+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG082+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 : Mon Jul 18 20:41:25 EDT 2022

% Result   : Theorem 0.47s 0.65s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   88 (   8 unt;   0 nHn;  88 RR)
%            Number of literals    :  284 (   0 equ; 201 neg)
%            Maximal clause size   :    5 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    aElement0(sz00),
    file('RNG082+1.p',unknown),
    [] ).

cnf(2,axiom,
    aElement0(sz10),
    file('RNG082+1.p',unknown),
    [] ).

cnf(3,axiom,
    aElement0(xx),
    file('RNG082+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ aElement0(u)
    | aElement0(smndt0(u)) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(sdtasdt0(smndt0(sz10),xx),smndt0(xx)),
    file('RNG082+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ aElement0(u)
    | equal(sdtpldt0(u,sz00),u) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ aElement0(u)
    | equal(sdtpldt0(sz00,u),u) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ aElement0(u)
    | equal(sdtasdt0(u,sz10),u) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ aElement0(u)
    | equal(sdtpldt0(u,smndt0(u)),sz00) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ aElement0(u)
    | equal(sdtpldt0(smndt0(u),u),sz00) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | aElement0(sdtpldt0(v,u)) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | aElement0(sdtasdt0(v,u)) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(w)
    | equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(w)
    | equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
    file('RNG082+1.p',unknown),
    [] ).

cnf(59,plain,
    ( ~ aElement0(xx)
    | ~ aElement0(smndt0(sz10))
    | ~ equal(sdtasdt0(xx,smndt0(sz10)),smndt0(xx)) ),
    inference(spl,[status(thm),theory(equality)],[15,5]),
    [iquote('0:SpL:15.2,5.0')] ).

cnf(65,plain,
    ~ equal(sdtasdt0(xx,smndt0(sz10)),smndt0(xx)),
    inference(ssi,[status(thm)],[59,4,2,3]),
    [iquote('0:SSi:59.1,59.0,4.0,2.0,3.1')] ).

cnf(95,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(u)
    | ~ aElement0(sz00)
    | equal(sdtpldt0(sz00,sdtpldt0(u,v)),sdtpldt0(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[7,17]),
    [iquote('0:SpR:7.1,17.3')] ).

cnf(96,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(u)
    | ~ aElement0(smndt0(u))
    | equal(sdtpldt0(smndt0(u),sdtpldt0(u,v)),sdtpldt0(sz00,v)) ),
    inference(spr,[status(thm),theory(equality)],[11,17]),
    [iquote('0:SpR:11.1,17.3')] ).

cnf(99,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(u))
    | ~ aElement0(u)
    | equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(sz00,v)) ),
    inference(spr,[status(thm),theory(equality)],[10,17]),
    [iquote('0:SpR:10.1,17.3')] ).

cnf(103,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(sz00)
    | equal(sdtpldt0(sz00,sdtpldt0(v,u)),sdtpldt0(v,u)) ),
    inference(obv,[status(thm),theory(equality)],[95]),
    [iquote('0:Obv:95.0')] ).

cnf(104,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(sz00,sdtpldt0(v,u)),sdtpldt0(v,u)) ),
    inference(ssi,[status(thm)],[103,1]),
    [iquote('0:SSi:103.2,1.0')] ).

cnf(105,plain,
    ( ~ aElement0(u)
    | ~ aElement0(smndt0(v))
    | ~ aElement0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
    inference(obv,[status(thm),theory(equality)],[99]),
    [iquote('0:Obv:99.0')] ).

cnf(106,plain,
    ( ~ aElement0(u)
    | ~ aElement0(smndt0(v))
    | ~ aElement0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
    inference(rew,[status(thm),theory(equality)],[7,105]),
    [iquote('0:Rew:7.1,105.3')] ).

cnf(107,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
    inference(ssi,[status(thm)],[106,4]),
    [iquote('0:SSi:106.1,4.1')] ).

cnf(108,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(v))
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
    inference(obv,[status(thm),theory(equality)],[96]),
    [iquote('0:Obv:96.0')] ).

cnf(109,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(v))
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
    inference(rew,[status(thm),theory(equality)],[7,108]),
    [iquote('0:Rew:7.1,108.3')] ).

cnf(110,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
    inference(ssi,[status(thm)],[109,4]),
    [iquote('0:SSi:109.2,4.1')] ).

cnf(134,plain,
    ( ~ aElement0(smndt0(u))
    | ~ aElement0(smndt0(smndt0(u)))
    | ~ aElement0(u)
    | equal(sdtpldt0(u,sz00),smndt0(smndt0(u))) ),
    inference(spr,[status(thm),theory(equality)],[10,107]),
    [iquote('0:SpR:10.1,107.2')] ).

cnf(135,plain,
    ( ~ aElement0(smndt0(u))
    | ~ aElement0(v)
    | ~ aElement0(v)
    | ~ aElement0(u)
    | equal(sdtpldt0(u,sdtpldt0(v,smndt0(u))),v) ),
    inference(spr,[status(thm),theory(equality)],[14,107]),
    [iquote('0:SpR:14.2,107.2')] ).

cnf(139,plain,
    ( ~ aElement0(smndt0(u))
    | ~ aElement0(smndt0(smndt0(u)))
    | ~ aElement0(u)
    | equal(smndt0(smndt0(u)),u) ),
    inference(rew,[status(thm),theory(equality)],[6,134]),
    [iquote('0:Rew:6.1,134.3')] ).

cnf(140,plain,
    ( ~ aElement0(u)
    | equal(smndt0(smndt0(u)),u) ),
    inference(ssi,[status(thm)],[139,4]),
    [iquote('0:SSi:139.1,139.0,4.1,4.1,4.1')] ).

cnf(141,plain,
    ( ~ aElement0(smndt0(u))
    | ~ aElement0(v)
    | ~ aElement0(u)
    | equal(sdtpldt0(u,sdtpldt0(v,smndt0(u))),v) ),
    inference(obv,[status(thm),theory(equality)],[135]),
    [iquote('0:Obv:135.1')] ).

cnf(142,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(v,sdtpldt0(u,smndt0(v))),u) ),
    inference(ssi,[status(thm)],[141,4]),
    [iquote('0:SSi:141.0,4.1')] ).

cnf(192,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(v)
    | ~ aElement0(u)
    | equal(sdtpldt0(smndt0(u),sdtpldt0(v,u)),v) ),
    inference(spr,[status(thm),theory(equality)],[14,110]),
    [iquote('0:SpR:14.2,110.2')] ).

cnf(203,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(smndt0(v),sdtpldt0(u,v)),u) ),
    inference(obv,[status(thm),theory(equality)],[192]),
    [iquote('0:Obv:192.1')] ).

cnf(213,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(sdtpldt0(u,smndt0(v)))
    | ~ aElement0(v)
    | equal(sdtpldt0(smndt0(v),u),sdtpldt0(u,smndt0(v))) ),
    inference(spr,[status(thm),theory(equality)],[142,110]),
    [iquote('0:SpR:142.2,110.2')] ).

cnf(234,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtpldt0(u,smndt0(v)))
    | ~ aElement0(v)
    | equal(sdtpldt0(smndt0(v),u),sdtpldt0(u,smndt0(v))) ),
    inference(obv,[status(thm),theory(equality)],[213]),
    [iquote('0:Obv:213.1')] ).

cnf(235,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(smndt0(v),u),sdtpldt0(u,smndt0(v))) ),
    inference(ssi,[status(thm)],[234,12,4]),
    [iquote('0:SSi:234.1,12.1,4.2')] ).

cnf(244,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(v))
    | ~ aElement0(sdtpldt0(u,v))
    | equal(sdtpldt0(smndt0(sdtpldt0(u,v)),u),smndt0(v)) ),
    inference(spr,[status(thm),theory(equality)],[203]),
    [iquote('0:SpR:203.2,203.2')] ).

cnf(257,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(v))
    | ~ aElement0(sdtpldt0(v,u))
    | equal(sdtpldt0(smndt0(sdtpldt0(v,u)),u),smndt0(v)) ),
    inference(spr,[status(thm),theory(equality)],[110,203]),
    [iquote('0:SpR:110.2,203.2')] ).

cnf(258,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(v)
    | ~ aElement0(sdtpldt0(u,smndt0(v)))
    | equal(sdtpldt0(smndt0(sdtpldt0(u,smndt0(v))),u),v) ),
    inference(spr,[status(thm),theory(equality)],[142,203]),
    [iquote('0:SpR:142.2,203.2')] ).

cnf(272,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(sdtpldt0(u,smndt0(v)))
    | equal(sdtpldt0(smndt0(sdtpldt0(u,smndt0(v))),u),v) ),
    inference(obv,[status(thm),theory(equality)],[258]),
    [iquote('0:Obv:258.1')] ).

cnf(273,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(sdtpldt0(u,smndt0(v)))
    | equal(sdtpldt0(u,smndt0(sdtpldt0(u,smndt0(v)))),v) ),
    inference(rew,[status(thm),theory(equality)],[235,272]),
    [iquote('0:Rew:235.2,272.3')] ).

cnf(274,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(u,smndt0(sdtpldt0(u,smndt0(v)))),v) ),
    inference(ssi,[status(thm)],[273,12,4]),
    [iquote('0:SSi:273.2,12.1,4.2')] ).

cnf(275,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(v))
    | ~ aElement0(sdtpldt0(v,u))
    | equal(sdtpldt0(u,smndt0(sdtpldt0(v,u))),smndt0(v)) ),
    inference(rew,[status(thm),theory(equality)],[235,257]),
    [iquote('0:Rew:235.2,257.4')] ).

cnf(276,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(u,smndt0(sdtpldt0(v,u))),smndt0(v)) ),
    inference(ssi,[status(thm)],[275,12,4]),
    [iquote('0:SSi:275.3,275.2,12.1,4.2')] ).

cnf(282,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(v))
    | ~ aElement0(sdtpldt0(u,v))
    | equal(sdtpldt0(u,smndt0(sdtpldt0(u,v))),smndt0(v)) ),
    inference(rew,[status(thm),theory(equality)],[235,244]),
    [iquote('0:Rew:235.2,244.4')] ).

cnf(283,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(u,smndt0(sdtpldt0(u,v))),smndt0(v)) ),
    inference(ssi,[status(thm)],[282,12,4]),
    [iquote('0:SSi:282.3,282.2,12.1,4.2')] ).

cnf(350,plain,
    ( ~ aElement0(u)
    | ~ aElement0(u)
    | ~ aElement0(smndt0(u))
    | equal(sdtpldt0(sz00,sz00),sz00) ),
    inference(spr,[status(thm),theory(equality)],[11,104]),
    [iquote('0:SpR:11.1,104.2')] ).

cnf(362,plain,
    ( ~ aElement0(u)
    | ~ aElement0(smndt0(u))
    | equal(sdtpldt0(sz00,sz00),sz00) ),
    inference(obv,[status(thm),theory(equality)],[350]),
    [iquote('0:Obv:350.0')] ).

cnf(363,plain,
    ( ~ aElement0(u)
    | equal(sdtpldt0(sz00,sz00),sz00) ),
    inference(ssi,[status(thm)],[362,4]),
    [iquote('0:SSi:362.1,4.1')] ).

cnf(379,plain,
    equal(sdtpldt0(sz00,sz00),sz00),
    inference(ems,[status(thm)],[363,1]),
    [iquote('0:EmS:363.0,1.0')] ).

cnf(454,plain,
    ( ~ aElement0(u)
    | ~ aElement0(smndt0(u))
    | ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,smndt0(u))),sdtasdt0(v,sz00)) ),
    inference(spr,[status(thm),theory(equality)],[10,19]),
    [iquote('0:SpR:10.1,19.3')] ).

cnf(461,plain,
    ( ~ aElement0(sz00)
    | ~ aElement0(sz00)
    | ~ aElement0(u)
    | equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
    inference(spr,[status(thm),theory(equality)],[379,19]),
    [iquote('0:SpR:379.0,19.3')] ).

cnf(462,plain,
    ( ~ aElement0(sz00)
    | ~ aElement0(u)
    | equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
    inference(obv,[status(thm),theory(equality)],[461]),
    [iquote('0:Obv:461.0')] ).

cnf(463,plain,
    ( ~ aElement0(u)
    | equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
    inference(ssi,[status(thm)],[462,1]),
    [iquote('0:SSi:462.0,1.0')] ).

cnf(468,plain,
    ( ~ aElement0(smndt0(u))
    | ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,smndt0(u))),sdtasdt0(v,sz00)) ),
    inference(obv,[status(thm),theory(equality)],[454]),
    [iquote('0:Obv:454.0')] ).

cnf(469,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,smndt0(u))),sdtasdt0(v,sz00)) ),
    inference(ssi,[status(thm)],[468,4]),
    [iquote('0:SSi:468.0,4.1')] ).

cnf(508,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtasdt0(u,sz00))
    | ~ aElement0(sdtasdt0(u,sz00))
    | equal(sdtpldt0(smndt0(sdtasdt0(u,sz00)),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
    inference(spr,[status(thm),theory(equality)],[463,203]),
    [iquote('0:SpR:463.1,203.2')] ).

cnf(530,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtasdt0(u,sz00))
    | equal(sdtpldt0(smndt0(sdtasdt0(u,sz00)),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
    inference(obv,[status(thm),theory(equality)],[508]),
    [iquote('0:Obv:508.1')] ).

cnf(531,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtasdt0(u,sz00))
    | equal(sdtasdt0(u,sz00),sz00) ),
    inference(rew,[status(thm),theory(equality)],[11,530]),
    [iquote('0:Rew:11.1,530.2')] ).

cnf(532,plain,
    ( ~ aElement0(u)
    | equal(sdtasdt0(u,sz00),sz00) ),
    inference(ssi,[status(thm)],[531,13,1]),
    [iquote('0:SSi:531.1,13.0,1.2')] ).

cnf(536,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,smndt0(u))),sz00) ),
    inference(rew,[status(thm),theory(equality)],[532,469]),
    [iquote('0:Rew:532.1,469.2')] ).

cnf(747,plain,
    ( ~ aElement0(sz00)
    | ~ aElement0(u)
    | ~ aElement0(smndt0(sdtpldt0(sz00,smndt0(u))))
    | equal(smndt0(sdtpldt0(sz00,smndt0(u))),u) ),
    inference(spr,[status(thm),theory(equality)],[274,7]),
    [iquote('0:SpR:274.2,7.1')] ).

cnf(748,plain,
    ( ~ aElement0(smndt0(u))
    | ~ aElement0(v)
    | ~ aElement0(smndt0(sdtpldt0(smndt0(u),smndt0(v))))
    | ~ aElement0(u)
    | equal(smndt0(sdtpldt0(smndt0(u),smndt0(v))),sdtpldt0(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[274,107]),
    [iquote('0:SpR:274.2,107.2')] ).

cnf(776,plain,
    ( ~ aElement0(u)
    | equal(smndt0(sdtpldt0(sz00,smndt0(u))),u) ),
    inference(ssi,[status(thm)],[747,4,12,1]),
    [iquote('0:SSi:747.2,747.0,4.0,12.1,1.0,4.2,1.1')] ).

cnf(795,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(smndt0(sdtpldt0(smndt0(v),smndt0(u))),sdtpldt0(v,u)) ),
    inference(ssi,[status(thm)],[748,4,12]),
    [iquote('0:SSi:748.2,748.0,4.1,12.1,4.1,4.2,4.1')] ).

cnf(804,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtpldt0(sz00,smndt0(u)))
    | equal(sdtpldt0(sz00,smndt0(u)),smndt0(u)) ),
    inference(spr,[status(thm),theory(equality)],[776,140]),
    [iquote('0:SpR:776.1,140.1')] ).

cnf(821,plain,
    ( ~ aElement0(u)
    | equal(sdtpldt0(sz00,smndt0(u)),smndt0(u)) ),
    inference(ssi,[status(thm)],[804,12,1,4]),
    [iquote('0:SSi:804.1,12.1,1.0,4.2')] ).

cnf(908,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(u)
    | ~ aElement0(smndt0(sdtpldt0(v,u)))
    | equal(sdtpldt0(smndt0(smndt0(sdtpldt0(v,u))),smndt0(v)),u) ),
    inference(spr,[status(thm),theory(equality)],[276,203]),
    [iquote('0:SpR:276.2,203.2')] ).

cnf(958,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(sdtpldt0(u,v)))
    | equal(sdtpldt0(smndt0(smndt0(sdtpldt0(u,v))),smndt0(u)),v) ),
    inference(obv,[status(thm),theory(equality)],[908]),
    [iquote('0:Obv:908.0')] ).

cnf(959,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(smndt0(smndt0(sdtpldt0(u,v))),smndt0(u)),v) ),
    inference(ssi,[status(thm)],[958,4,12]),
    [iquote('0:SSi:958.2,4.2,12.1')] ).

cnf(1075,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(smndt0(v))
    | ~ aElement0(sdtpldt0(v,u))
    | equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
    inference(spr,[status(thm),theory(equality)],[110,283]),
    [iquote('0:SpR:110.2,283.2')] ).

cnf(1108,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
    inference(ssi,[status(thm)],[1075,12,4]),
    [iquote('0:SSi:1075.3,1075.2,12.1,4.2')] ).

cnf(1109,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(smndt0(smndt0(sdtpldt0(v,u))),sdtpldt0(v,u)) ),
    inference(rew,[status(thm),theory(equality)],[1108,795]),
    [iquote('0:Rew:1108.2,795.2')] ).

cnf(1111,plain,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(sdtpldt0(u,v),smndt0(u)),v) ),
    inference(rew,[status(thm),theory(equality)],[1109,959]),
    [iquote('0:Rew:1109.2,959.2')] ).

cnf(1375,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sz10)
    | ~ aElement0(u)
    | equal(sdtpldt0(u,sdtasdt0(u,smndt0(sz10))),sz00) ),
    inference(spr,[status(thm),theory(equality)],[8,536]),
    [iquote('0:SpR:8.1,536.2')] ).

cnf(1388,plain,
    ( ~ aElement0(sz10)
    | ~ aElement0(u)
    | equal(sdtpldt0(u,sdtasdt0(u,smndt0(sz10))),sz00) ),
    inference(obv,[status(thm),theory(equality)],[1375]),
    [iquote('0:Obv:1375.0')] ).

cnf(1389,plain,
    ( ~ aElement0(u)
    | equal(sdtpldt0(u,sdtasdt0(u,smndt0(sz10))),sz00) ),
    inference(ssi,[status(thm)],[1388,2]),
    [iquote('0:SSi:1388.0,2.0')] ).

cnf(1772,plain,
    ( ~ aElement0(u)
    | ~ aElement0(u)
    | ~ aElement0(sdtasdt0(u,smndt0(sz10)))
    | equal(sdtasdt0(u,smndt0(sz10)),sdtpldt0(sz00,smndt0(u))) ),
    inference(spr,[status(thm),theory(equality)],[1389,1111]),
    [iquote('0:SpR:1389.1,1111.2')] ).

cnf(1796,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtasdt0(u,smndt0(sz10)))
    | equal(sdtasdt0(u,smndt0(sz10)),sdtpldt0(sz00,smndt0(u))) ),
    inference(obv,[status(thm),theory(equality)],[1772]),
    [iquote('0:Obv:1772.0')] ).

cnf(1797,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtasdt0(u,smndt0(sz10)))
    | equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
    inference(rew,[status(thm),theory(equality)],[821,1796]),
    [iquote('0:Rew:821.1,1796.2')] ).

cnf(1798,plain,
    ( ~ aElement0(u)
    | equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
    inference(ssi,[status(thm)],[1797,13,4,2]),
    [iquote('0:SSi:1797.1,13.0,4.1,2.2')] ).

cnf(1938,plain,
    ( ~ aElement0(xx)
    | ~ equal(smndt0(xx),smndt0(xx)) ),
    inference(spl,[status(thm),theory(equality)],[1798,65]),
    [iquote('0:SpL:1798.1,65.0')] ).

cnf(1939,plain,
    ~ aElement0(xx),
    inference(obv,[status(thm),theory(equality)],[1938]),
    [iquote('0:Obv:1938.1')] ).

cnf(1940,plain,
    $false,
    inference(ssi,[status(thm)],[1939,3]),
    [iquote('0:SSi:1939.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : RNG082+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n026.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 : Mon May 30 05:32:40 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.47/0.65  
% 0.47/0.65  SPASS V 3.9 
% 0.47/0.65  SPASS beiseite: Proof found.
% 0.47/0.65  % SZS status Theorem
% 0.47/0.65  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.47/0.65  SPASS derived 1001 clauses, backtracked 0 clauses, performed 0 splits and kept 203 clauses.
% 0.47/0.65  SPASS allocated 105915 KBytes.
% 0.47/0.65  SPASS spent	0:00:00.30 on the problem.
% 0.47/0.65  		0:00:00.04 for the input.
% 0.47/0.65  		0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.65  		0:00:00.01 for inferences.
% 0.47/0.65  		0:00:00.00 for the backtracking.
% 0.47/0.65  		0:00:00.20 for the reduction.
% 0.47/0.65  
% 0.47/0.65  
% 0.47/0.65  Here is a proof with depth 6, length 88 :
% 0.47/0.65  % SZS output start Refutation
% See solution above
% 0.47/0.70  Formulae used in the proof : mSortsC mSortsC_01 m__444 mSortsU m__ mAddZero mMulUnit mAddInvr mSortsB mSortsB_02 mAddComm mMulComm mAddAsso mAMDistr
% 0.47/0.70  
%------------------------------------------------------------------------------