TSTP Solution File: NUM454+6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM454+6 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 14:26:21 EDT 2022

% Result   : Theorem 77.39s 77.57s
% Output   : Refutation 90.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   68
%            Number of leaves      :   30
% Syntax   : Number of clauses     :  265 (  62 unt;  11 nHn; 265 RR)
%            Number of literals    :  708 (   0 equ; 438 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    aInteger0(sz00),
    file('NUM454+6.p',unknown),
    [] ).

cnf(2,axiom,
    aInteger0(sz10),
    file('NUM454+6.p',unknown),
    [] ).

cnf(5,axiom,
    aInteger0(xp),
    file('NUM454+6.p',unknown),
    [] ).

cnf(6,axiom,
    aInteger0(skc43),
    file('NUM454+6.p',unknown),
    [] ).

cnf(7,axiom,
    aInteger0(skc42),
    file('NUM454+6.p',unknown),
    [] ).

cnf(25,axiom,
    ~ equal(xp,sz00),
    file('NUM454+6.p',unknown),
    [] ).

cnf(28,axiom,
    equal(sdtpldt0(sz10,xp),smndt0(sz10)),
    file('NUM454+6.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ aInteger0(u)
    | aInteger0(smndt0(u)) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(33,axiom,
    equal(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
    file('NUM454+6.p',unknown),
    [] ).

cnf(41,axiom,
    aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
    file('NUM454+6.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,sz00),u) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(sz00,u),u) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(u,sz10),u) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(sz10,u),u) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(49,axiom,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(sz00,u),sz00) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ aElementOf0(u,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    | aInteger0(u) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,smndt0(u)),sz00) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(u),u),sz00) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | aInteger0(sdtpldt0(v,u)) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | aInteger0(sdtasdt0(v,u)) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(smndt0(sz10),u),smndt0(u)) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(90,axiom,
    equal(sdtasdt0(xp,skc42),sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))),
    file('NUM454+6.p',unknown),
    [] ).

cnf(104,axiom,
    equal(sdtasdt0(xp,skc43),sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))),
    file('NUM454+6.p',unknown),
    [] ).

cnf(109,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(148,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ equal(sdtasdt0(v,u),sz00)
    | equal(u,sz00)
    | equal(v,sz00) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(168,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(169,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(184,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | equal(sdtasdt0(sdtpldt0(w,v),u),sdtpldt0(sdtasdt0(w,u),sdtasdt0(v,u))) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(185,axiom,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
    file('NUM454+6.p',unknown),
    [] ).

cnf(217,plain,
    aElementOf0(smndt0(sz10),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
    inference(rew,[status(thm),theory(equality)],[28,41]),
    [iquote('0:Rew:28.0,41.0')] ).

cnf(228,plain,
    equal(sdtasdt0(xp,skc42),sdtpldt0(smndt0(sz10),smndt0(sz10))),
    inference(rew,[status(thm),theory(equality)],[28,90]),
    [iquote('0:Rew:28.0,90.0')] ).

cnf(231,plain,
    equal(sdtasdt0(xp,skc43),sdtpldt0(smndt0(sz10),smndt0(sz10))),
    inference(rew,[status(thm),theory(equality)],[33,104]),
    [iquote('0:Rew:33.0,104.0')] ).

cnf(288,plain,
    aInteger0(smndt0(sz10)),
    inference(res,[status(thm),theory(equality)],[217,54]),
    [iquote('0:Res:217.0,54.0')] ).

cnf(707,plain,
    ( ~ aInteger0(skc42)
    | ~ aInteger0(xp)
    | aInteger0(sdtpldt0(smndt0(sz10),smndt0(sz10))) ),
    inference(spr,[status(thm),theory(equality)],[228,78]),
    [iquote('0:SpR:228.0,78.2')] ).

cnf(709,plain,
    aInteger0(sdtpldt0(smndt0(sz10),smndt0(sz10))),
    inference(ssi,[status(thm)],[707,5,7]),
    [iquote('0:SSi:707.1,707.0,5.0,7.0')] ).

cnf(7625,plain,
    ( ~ aInteger0(smndt0(sdtpldt0(u,v)))
    | ~ aInteger0(v)
    | ~ aInteger0(u)
    | ~ aInteger0(sdtpldt0(u,v))
    | equal(sdtpldt0(u,sdtpldt0(v,smndt0(sdtpldt0(u,v)))),sz00) ),
    inference(spr,[status(thm),theory(equality)],[169,58]),
    [iquote('0:SpR:169.3,58.1')] ).

cnf(7653,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(u)
    | ~ aInteger0(smndt0(u))
    | equal(sdtpldt0(smndt0(u),sdtpldt0(u,v)),sdtpldt0(sz00,v)) ),
    inference(spr,[status(thm),theory(equality)],[59,169]),
    [iquote('0:SpR:59.1,169.3')] ).

cnf(7656,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | ~ aInteger0(v)
    | ~ aInteger0(u)
    | equal(sdtpldt0(sdtpldt0(v,u),w),sdtpldt0(u,sdtpldt0(v,w))) ),
    inference(spr,[status(thm),theory(equality)],[109,169]),
    [iquote('0:SpR:109.2,169.3')] ).

cnf(7657,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(xp)
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),u),sdtpldt0(sz10,sdtpldt0(xp,u))) ),
    inference(spr,[status(thm),theory(equality)],[28,169]),
    [iquote('0:SpR:28.0,169.3')] ).

cnf(7659,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(smndt0(u))
    | ~ aInteger0(u)
    | equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(sz00,v)) ),
    inference(spr,[status(thm),theory(equality)],[58,169]),
    [iquote('0:SpR:58.1,169.3')] ).

cnf(7711,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(sz10),u),sdtpldt0(sz10,sdtpldt0(xp,u))) ),
    inference(ssi,[status(thm)],[7657,2,5]),
    [iquote('0:SSi:7657.2,7657.1,2.0,5.0')] ).

cnf(7730,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(v))
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
    inference(obv,[status(thm),theory(equality)],[7659]),
    [iquote('0:Obv:7659.0')] ).

cnf(7731,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(v))
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
    inference(rew,[status(thm),theory(equality)],[45,7730]),
    [iquote('0:Rew:45.1,7730.3')] ).

cnf(7732,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
    inference(ssi,[status(thm)],[7731,29]),
    [iquote('0:SSi:7731.1,29.1')] ).

cnf(7733,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(smndt0(v))
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
    inference(obv,[status(thm),theory(equality)],[7653]),
    [iquote('0:Obv:7653.0')] ).

cnf(7734,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(smndt0(v))
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
    inference(rew,[status(thm),theory(equality)],[45,7733]),
    [iquote('0:Rew:45.1,7733.3')] ).

cnf(7735,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
    inference(ssi,[status(thm)],[7734,29]),
    [iquote('0:SSi:7734.2,29.1')] ).

cnf(7739,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | equal(sdtpldt0(sdtpldt0(v,w),u),sdtpldt0(w,sdtpldt0(v,u))) ),
    inference(obv,[status(thm),theory(equality)],[7656]),
    [iquote('0:Obv:7656.1')] ).

cnf(7740,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | equal(sdtpldt0(v,sdtpldt0(w,u)),sdtpldt0(w,sdtpldt0(v,u))) ),
    inference(rew,[status(thm),theory(equality)],[169,7739]),
    [iquote('0:Rew:169.3,7739.3')] ).

cnf(7743,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,sdtpldt0(u,smndt0(sdtpldt0(v,u)))),sz00) ),
    inference(ssi,[status(thm)],[7625,77,29]),
    [iquote('0:SSi:7625.3,7625.0,77.2,29.1,77.2')] ).

cnf(7851,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(sdtasdt0(v,u))
    | equal(sdtasdt0(v,sdtasdt0(u,smndt0(sz10))),smndt0(sdtasdt0(v,u))) ),
    inference(spr,[status(thm),theory(equality)],[168,80]),
    [iquote('0:SpR:168.3,80.1')] ).

cnf(7860,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(u)
    | equal(sdtasdt0(smndt0(u),v),sdtasdt0(u,sdtasdt0(smndt0(sz10),v))) ),
    inference(spr,[status(thm),theory(equality)],[80,168]),
    [iquote('0:SpR:80.1,168.3')] ).

cnf(7866,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(skc42)
    | ~ aInteger0(xp)
    | equal(sdtasdt0(sdtpldt0(smndt0(sz10),smndt0(sz10)),u),sdtasdt0(xp,sdtasdt0(skc42,u))) ),
    inference(spr,[status(thm),theory(equality)],[228,168]),
    [iquote('0:SpR:228.0,168.3')] ).

cnf(7867,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(skc43)
    | ~ aInteger0(xp)
    | equal(sdtasdt0(sdtpldt0(smndt0(sz10),smndt0(sz10)),u),sdtasdt0(xp,sdtasdt0(skc43,u))) ),
    inference(spr,[status(thm),theory(equality)],[231,168]),
    [iquote('0:SpR:231.0,168.3')] ).

cnf(7882,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(sdtpldt0(smndt0(sz10),smndt0(sz10)),u),sdtasdt0(xp,sdtasdt0(skc43,u))) ),
    inference(ssi,[status(thm)],[7867,5,6]),
    [iquote('0:SSi:7867.2,7867.1,5.0,6.0')] ).

cnf(7883,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(skc42)
    | ~ aInteger0(xp)
    | equal(sdtasdt0(xp,sdtasdt0(skc43,u)),sdtasdt0(xp,sdtasdt0(skc42,u))) ),
    inference(rew,[status(thm),theory(equality)],[7882,7866]),
    [iquote('0:Rew:7882.1,7866.3')] ).

cnf(7884,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(xp,sdtasdt0(skc43,u)),sdtasdt0(xp,sdtasdt0(skc42,u))) ),
    inference(ssi,[status(thm)],[7883,5,7]),
    [iquote('0:SSi:7883.2,7883.1,5.0,7.0')] ).

cnf(7885,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(sdtpldt0(smndt0(sz10),smndt0(sz10)),u),sdtasdt0(xp,sdtasdt0(skc42,u))) ),
    inference(rew,[status(thm),theory(equality)],[7884,7882]),
    [iquote('0:Rew:7884.1,7882.1')] ).

cnf(7891,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(v)
    | equal(sdtasdt0(smndt0(v),u),sdtasdt0(v,sdtasdt0(smndt0(sz10),u))) ),
    inference(obv,[status(thm),theory(equality)],[7860]),
    [iquote('0:Obv:7860.0')] ).

cnf(7892,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(v)
    | equal(sdtasdt0(smndt0(v),u),sdtasdt0(v,smndt0(u))) ),
    inference(rew,[status(thm),theory(equality)],[79,7891]),
    [iquote('0:Rew:79.1,7891.3')] ).

cnf(7893,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtasdt0(smndt0(v),u),sdtasdt0(v,smndt0(u))) ),
    inference(ssi,[status(thm)],[7892,288]),
    [iquote('0:SSi:7892.1,288.0')] ).

cnf(7901,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(sdtasdt0(v,u))
    | equal(sdtasdt0(v,smndt0(u)),smndt0(sdtasdt0(v,u))) ),
    inference(rew,[status(thm),theory(equality)],[80,7851]),
    [iquote('0:Rew:80.1,7851.4')] ).

cnf(7902,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtasdt0(v,smndt0(u)),smndt0(sdtasdt0(v,u))) ),
    inference(ssi,[status(thm)],[7901,78,288]),
    [iquote('0:SSi:7901.3,7901.0,78.0,288.2')] ).

cnf(7903,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtasdt0(smndt0(v),u),smndt0(sdtasdt0(v,u))) ),
    inference(rew,[status(thm),theory(equality)],[7902,7893]),
    [iquote('0:Rew:7902.2,7893.2')] ).

cnf(8493,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(sdtpldt0(v,u))
    | equal(sdtpldt0(sdtasdt0(v,smndt0(sz10)),sdtasdt0(u,smndt0(sz10))),smndt0(sdtpldt0(v,u))) ),
    inference(spr,[status(thm),theory(equality)],[184,80]),
    [iquote('0:SpR:184.3,80.1')] ).

cnf(8506,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(xp)
    | ~ aInteger0(sz10)
    | equal(sdtasdt0(smndt0(sz10),u),sdtpldt0(sdtasdt0(sz10,u),sdtasdt0(xp,u))) ),
    inference(spr,[status(thm),theory(equality)],[28,184]),
    [iquote('0:SpR:28.0,184.3')] ).

cnf(8511,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(xp)
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(u,sdtasdt0(xp,u)),smndt0(u)) ),
    inference(rew,[status(thm),theory(equality)],[79,8506,47]),
    [iquote('0:Rew:79.1,8506.3,47.1,8506.3')] ).

cnf(8512,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,sdtasdt0(xp,u)),smndt0(u)) ),
    inference(ssi,[status(thm)],[8511,2,5]),
    [iquote('0:SSi:8511.2,8511.1,2.0,5.0')] ).

cnf(8537,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(sdtpldt0(v,u))
    | equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
    inference(rew,[status(thm),theory(equality)],[80,8493]),
    [iquote('0:Rew:80.1,8493.4,80.1,8493.4')] ).

cnf(8538,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
    inference(ssi,[status(thm)],[8537,77,288]),
    [iquote('0:SSi:8537.3,8537.0,77.0,288.2')] ).

cnf(8601,plain,
    ( ~ aInteger0(smndt0(xp))
    | ~ aInteger0(sz10)
    | ~ aInteger0(u)
    | equal(sdtpldt0(sdtasdt0(u,sz10),sdtasdt0(u,smndt0(xp))),sdtasdt0(u,smndt0(sz10))) ),
    inference(spr,[status(thm),theory(equality)],[33,185]),
    [iquote('0:SpR:33.0,185.3')] ).

cnf(8603,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | ~ aInteger0(sdtpldt0(v,u))
    | ~ aInteger0(w)
    | ~ equal(sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u)),sz00)
    | equal(sdtpldt0(v,u),sz00)
    | equal(w,sz00) ),
    inference(spl,[status(thm),theory(equality)],[185,148]),
    [iquote('0:SpL:185.3,148.2')] ).

cnf(8609,plain,
    ( ~ aInteger0(smndt0(xp))
    | ~ aInteger0(sz10)
    | ~ aInteger0(u)
    | equal(sdtpldt0(u,sdtasdt0(u,smndt0(xp))),smndt0(u)) ),
    inference(rew,[status(thm),theory(equality)],[46,8601,80]),
    [iquote('0:Rew:46.1,8601.3,80.1,8601.3')] ).

cnf(8610,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,sdtasdt0(u,smndt0(xp))),smndt0(u)) ),
    inference(ssi,[status(thm)],[8609,2,29,5]),
    [iquote('0:SSi:8609.1,8609.0,2.0,29.1,5.0')] ).

cnf(8635,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(sdtpldt0(v,u))
    | ~ aInteger0(w)
    | ~ equal(sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u)),sz00)
    | equal(sdtpldt0(v,u),sz00)
    | equal(w,sz00) ),
    inference(obv,[status(thm),theory(equality)],[8603]),
    [iquote('0:Obv:8603.2')] ).

cnf(8636,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | ~ aInteger0(w)
    | ~ equal(sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u)),sz00)
    | equal(sdtpldt0(v,u),sz00)
    | equal(w,sz00) ),
    inference(ssi,[status(thm)],[8635,77]),
    [iquote('0:SSi:8635.2,77.2')] ).

cnf(9367,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(smndt0(sz10),smndt0(xp)),smndt0(smndt0(sz10))) ),
    inference(spr,[status(thm),theory(equality)],[80,8512]),
    [iquote('0:SpR:80.1,8512.1')] ).

cnf(9371,plain,
    ( ~ aInteger0(skc43)
    | equal(sdtpldt0(skc43,sdtpldt0(smndt0(sz10),smndt0(sz10))),smndt0(skc43)) ),
    inference(spr,[status(thm),theory(equality)],[231,8512]),
    [iquote('0:SpR:231.0,8512.1')] ).

cnf(9377,plain,
    equal(sdtpldt0(skc43,sdtpldt0(smndt0(sz10),smndt0(sz10))),smndt0(skc43)),
    inference(ssi,[status(thm)],[9371,6]),
    [iquote('0:SSi:9371.0,6.0')] ).

cnf(9381,plain,
    equal(sdtpldt0(smndt0(sz10),smndt0(xp)),smndt0(smndt0(sz10))),
    inference(ssi,[status(thm)],[9367,288,5]),
    [iquote('0:SSi:9367.1,9367.0,288.0,5.0')] ).

cnf(9417,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtasdt0(smndt0(smndt0(sz10)),u),sdtpldt0(sdtasdt0(smndt0(sz10),u),sdtasdt0(smndt0(xp),u))) ),
    inference(spr,[status(thm),theory(equality)],[9381,184]),
    [iquote('0:SpR:9381.0,184.3')] ).

cnf(9425,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtasdt0(smndt0(smndt0(sz10)),u),sdtpldt0(smndt0(u),sdtasdt0(smndt0(xp),u))) ),
    inference(rew,[status(thm),theory(equality)],[79,9417]),
    [iquote('0:Rew:79.1,9417.3')] ).

cnf(9426,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(smndt0(u),sdtasdt0(smndt0(xp),u)),smndt0(sdtasdt0(smndt0(sz10),u))) ),
    inference(rew,[status(thm),theory(equality)],[7903,9425]),
    [iquote('0:Rew:7903.2,9425.3')] ).

cnf(9427,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(smndt0(u),sdtasdt0(smndt0(xp),u)),smndt0(smndt0(u))) ),
    inference(rew,[status(thm),theory(equality)],[79,9426]),
    [iquote('0:Rew:79.1,9426.3')] ).

cnf(9428,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(u),sdtasdt0(smndt0(xp),u)),smndt0(smndt0(u))) ),
    inference(ssi,[status(thm)],[9427,288,29,5]),
    [iquote('0:SSi:9427.2,9427.1,288.0,29.1,5.0')] ).

cnf(9449,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sdtpldt0(smndt0(sz10),smndt0(sz10)))
    | ~ aInteger0(skc43)
    | equal(sdtpldt0(skc43,sdtpldt0(sdtpldt0(smndt0(sz10),smndt0(sz10)),u)),sdtpldt0(smndt0(skc43),u)) ),
    inference(spr,[status(thm),theory(equality)],[9377,169]),
    [iquote('0:SpR:9377.0,169.3')] ).

cnf(9456,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(skc43,sdtpldt0(sdtpldt0(smndt0(sz10),smndt0(sz10)),u)),sdtpldt0(smndt0(skc43),u)) ),
    inference(ssi,[status(thm)],[9449,6,709]),
    [iquote('0:SSi:9449.2,9449.1,6.0,709.0')] ).

cnf(14759,plain,
    ( ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(smndt0(sz10),smndt0(smndt0(xp))),smndt0(smndt0(sz10))) ),
    inference(spr,[status(thm),theory(equality)],[79,8610]),
    [iquote('0:SpR:79.1,8610.1')] ).

cnf(14767,plain,
    equal(sdtpldt0(smndt0(sz10),smndt0(smndt0(xp))),smndt0(smndt0(sz10))),
    inference(ssi,[status(thm)],[14759,288,29,5]),
    [iquote('0:SSi:14759.1,14759.0,288.0,29.1,5.0')] ).

cnf(14993,plain,
    ( ~ aInteger0(sz10)
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sz10,sdtpldt0(xp,sz10)),sz00) ),
    inference(spr,[status(thm),theory(equality)],[7711,59]),
    [iquote('0:SpR:7711.1,59.1')] ).

cnf(15015,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(u)
    | equal(sdtpldt0(u,smndt0(sz10)),sdtpldt0(sz10,sdtpldt0(xp,u))) ),
    inference(spr,[status(thm),theory(equality)],[7711,109]),
    [iquote('0:SpR:7711.1,109.2')] ).

cnf(15020,plain,
    ( ~ aInteger0(smndt0(xp))
    | equal(sdtpldt0(sz10,sdtpldt0(xp,smndt0(xp))),smndt0(smndt0(sz10))) ),
    inference(spr,[status(thm),theory(equality)],[7711,9381]),
    [iquote('0:SpR:7711.1,9381.0')] ).

cnf(15036,plain,
    ( ~ aInteger0(sz10)
    | equal(sdtpldt0(sz10,sdtpldt0(xp,sz10)),sz00) ),
    inference(obv,[status(thm),theory(equality)],[14993]),
    [iquote('0:Obv:14993.0')] ).

cnf(15037,plain,
    equal(sdtpldt0(sz10,sdtpldt0(xp,sz10)),sz00),
    inference(ssi,[status(thm)],[15036,2]),
    [iquote('0:SSi:15036.0,2.0')] ).

cnf(15038,plain,
    equal(sdtpldt0(sz10,sdtpldt0(xp,smndt0(xp))),smndt0(smndt0(sz10))),
    inference(ssi,[status(thm)],[15020,29,5]),
    [iquote('0:SSi:15020.0,29.0,5.1')] ).

cnf(15048,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(u)
    | equal(sdtpldt0(u,smndt0(sz10)),sdtpldt0(sz10,sdtpldt0(xp,u))) ),
    inference(obv,[status(thm),theory(equality)],[15015]),
    [iquote('0:Obv:15015.0')] ).

cnf(15049,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,smndt0(sz10)),sdtpldt0(sz10,sdtpldt0(xp,u))) ),
    inference(ssi,[status(thm)],[15048,288]),
    [iquote('0:SSi:15048.0,288.0')] ).

cnf(15175,plain,
    ( ~ aInteger0(xp)
    | equal(sdtpldt0(sz10,sz00),smndt0(smndt0(sz10))) ),
    inference(spr,[status(thm),theory(equality)],[58,15038]),
    [iquote('0:SpR:58.1,15038.0')] ).

cnf(15177,plain,
    equal(sdtpldt0(sz10,sz00),smndt0(smndt0(sz10))),
    inference(ssi,[status(thm)],[15175,5]),
    [iquote('0:SSi:15175.0,5.0')] ).

cnf(15202,plain,
    ( ~ aInteger0(sz10)
    | equal(smndt0(smndt0(sz10)),sz10) ),
    inference(spr,[status(thm),theory(equality)],[15177,44]),
    [iquote('0:SpR:15177.0,44.1')] ).

cnf(15222,plain,
    equal(smndt0(smndt0(sz10)),sz10),
    inference(ssi,[status(thm)],[15202,2]),
    [iquote('0:SSi:15202.0,2.0')] ).

cnf(15225,plain,
    equal(sdtpldt0(smndt0(sz10),smndt0(xp)),sz10),
    inference(rew,[status(thm),theory(equality)],[15222,9381]),
    [iquote('0:Rew:15222.0,9381.0')] ).

cnf(15232,plain,
    equal(sdtpldt0(smndt0(sz10),smndt0(smndt0(xp))),sz10),
    inference(rew,[status(thm),theory(equality)],[15222,14767]),
    [iquote('0:Rew:15222.0,14767.0')] ).

cnf(15236,plain,
    equal(sdtpldt0(sz10,sz00),sz10),
    inference(rew,[status(thm),theory(equality)],[15222,15177]),
    [iquote('0:Rew:15222.0,15177.0')] ).

cnf(15288,plain,
    ( ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(sz10,smndt0(sz10)),sz00) ),
    inference(spr,[status(thm),theory(equality)],[15222,59]),
    [iquote('0:SpR:15222.0,59.1')] ).

cnf(15289,plain,
    ( ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(smndt0(sz10),sz10),sz00) ),
    inference(spr,[status(thm),theory(equality)],[15222,58]),
    [iquote('0:SpR:15222.0,58.1')] ).

cnf(15296,plain,
    equal(sdtpldt0(sz10,smndt0(sz10)),sz00),
    inference(ssi,[status(thm)],[15288,288]),
    [iquote('0:SSi:15288.0,288.0')] ).

cnf(15300,plain,
    equal(sdtpldt0(smndt0(sz10),sz10),sz00),
    inference(ssi,[status(thm)],[15289,288]),
    [iquote('0:SSi:15289.0,288.0')] ).

cnf(15393,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(sdtasdt0(smndt0(sz10),u),sdtasdt0(smndt0(xp),u)),sdtasdt0(sz10,u)) ),
    inference(spr,[status(thm),theory(equality)],[15225,184]),
    [iquote('0:SpR:15225.0,184.3')] ).

cnf(15397,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(smndt0(u),sdtasdt0(smndt0(xp),u)),u) ),
    inference(rew,[status(thm),theory(equality)],[79,15393,47]),
    [iquote('0:Rew:79.1,15393.3,47.1,15393.3')] ).

cnf(15398,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(smndt0(smndt0(u)),u) ),
    inference(rew,[status(thm),theory(equality)],[9428,15397]),
    [iquote('0:Rew:9428.1,15397.3')] ).

cnf(15399,plain,
    ( ~ aInteger0(u)
    | equal(smndt0(smndt0(u)),u) ),
    inference(ssi,[status(thm)],[15398,288,29,5]),
    [iquote('0:SSi:15398.2,15398.1,288.0,29.1,5.0')] ).

cnf(15458,plain,
    ( ~ aInteger0(xp)
    | equal(sdtpldt0(smndt0(sz10),xp),sz10) ),
    inference(spr,[status(thm),theory(equality)],[15399,15232]),
    [iquote('0:SpR:15399.1,15232.0')] ).

cnf(15467,plain,
    ( ~ aInteger0(xp)
    | equal(sdtpldt0(sz10,sdtpldt0(xp,xp)),sz10) ),
    inference(rew,[status(thm),theory(equality)],[7711,15458]),
    [iquote('0:Rew:7711.1,15458.1')] ).

cnf(15468,plain,
    equal(sdtpldt0(sz10,sdtpldt0(xp,xp)),sz10),
    inference(ssi,[status(thm)],[15467,5]),
    [iquote('0:SSi:15467.0,5.0')] ).

cnf(16968,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sdtasdt0(xp,u))
    | ~ aInteger0(u)
    | equal(sdtasdt0(xp,u),sdtpldt0(smndt0(u),smndt0(u))) ),
    inference(spr,[status(thm),theory(equality)],[8512,7735]),
    [iquote('0:SpR:8512.1,7735.2')] ).

cnf(16972,plain,
    ( ~ aInteger0(smndt0(xp))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),smndt0(sz10)),smndt0(xp)) ),
    inference(spr,[status(thm),theory(equality)],[33,7735]),
    [iquote('0:SpR:33.0,7735.2')] ).

cnf(16973,plain,
    ( ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(smndt0(smndt0(sz10)),sz10),smndt0(xp)) ),
    inference(spr,[status(thm),theory(equality)],[15225,7735]),
    [iquote('0:SpR:15225.0,7735.2')] ).

cnf(16975,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),smndt0(sz10)),xp) ),
    inference(spr,[status(thm),theory(equality)],[28,7735]),
    [iquote('0:SpR:28.0,7735.2')] ).

cnf(16978,plain,
    ( ~ aInteger0(sdtpldt0(smndt0(sz10),smndt0(sz10)))
    | ~ aInteger0(skc43)
    | equal(sdtpldt0(smndt0(skc43),smndt0(skc43)),sdtpldt0(smndt0(sz10),smndt0(sz10))) ),
    inference(spr,[status(thm),theory(equality)],[9377,7735]),
    [iquote('0:SpR:9377.0,7735.2')] ).

cnf(16980,plain,
    ( ~ aInteger0(sdtpldt0(xp,sz10))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),sz00),sdtpldt0(xp,sz10)) ),
    inference(spr,[status(thm),theory(equality)],[15037,7735]),
    [iquote('0:SpR:15037.0,7735.2')] ).

cnf(16984,plain,
    ( ~ aInteger0(sdtpldt0(xp,xp))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),sz10),sdtpldt0(xp,xp)) ),
    inference(spr,[status(thm),theory(equality)],[15468,7735]),
    [iquote('0:SpR:15468.0,7735.2')] ).

cnf(16995,plain,
    equal(sdtpldt0(smndt0(sz10),smndt0(sz10)),xp),
    inference(ssi,[status(thm)],[16975,2,5]),
    [iquote('0:SSi:16975.1,16975.0,2.0,5.0')] ).

cnf(16998,plain,
    equal(sdtasdt0(xp,skc43),xp),
    inference(rew,[status(thm),theory(equality)],[16995,231]),
    [iquote('0:Rew:16995.0,231.0')] ).

cnf(17000,plain,
    equal(sdtpldt0(skc43,xp),smndt0(skc43)),
    inference(rew,[status(thm),theory(equality)],[16995,9377]),
    [iquote('0:Rew:16995.0,9377.0')] ).

cnf(17013,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(xp,sdtasdt0(skc42,u)),sdtasdt0(xp,u)) ),
    inference(rew,[status(thm),theory(equality)],[16995,7885]),
    [iquote('0:Rew:16995.0,7885.1')] ).

cnf(17014,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(skc43),u),sdtpldt0(skc43,sdtpldt0(xp,u))) ),
    inference(rew,[status(thm),theory(equality)],[16995,9456]),
    [iquote('0:Rew:16995.0,9456.1')] ).

cnf(17026,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(xp,sdtasdt0(skc43,u)),sdtasdt0(xp,u)) ),
    inference(rew,[status(thm),theory(equality)],[17013,7884]),
    [iquote('0:Rew:17013.1,7884.1')] ).

cnf(17046,plain,
    ( ~ aInteger0(smndt0(xp))
    | ~ aInteger0(sz10)
    | equal(smndt0(xp),xp) ),
    inference(rew,[status(thm),theory(equality)],[16995,16972]),
    [iquote('0:Rew:16995.0,16972.2')] ).

cnf(17047,plain,
    equal(smndt0(xp),xp),
    inference(ssi,[status(thm)],[17046,2,29,5]),
    [iquote('0:SSi:17046.1,17046.0,2.0,29.1,5.0')] ).

cnf(17103,plain,
    ( ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(sz10,sz10),smndt0(xp)) ),
    inference(rew,[status(thm),theory(equality)],[15222,16973]),
    [iquote('0:Rew:15222.0,16973.2')] ).

cnf(17104,plain,
    ( ~ aInteger0(smndt0(xp))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(sz10,sz10),xp) ),
    inference(rew,[status(thm),theory(equality)],[17047,17103]),
    [iquote('0:Rew:17047.0,17103.2')] ).

cnf(17105,plain,
    equal(sdtpldt0(sz10,sz10),xp),
    inference(ssi,[status(thm)],[17104,288,29,5]),
    [iquote('0:SSi:17104.1,17104.0,288.0,29.1,5.0')] ).

cnf(17109,plain,
    equal(sdtpldt0(smndt0(sz10),sz00),sdtpldt0(xp,sz10)),
    inference(ssi,[status(thm)],[16980,2,77,5]),
    [iquote('0:SSi:16980.1,16980.0,2.0,77.0,5.2,2.0')] ).

cnf(17110,plain,
    ( ~ aInteger0(sdtpldt0(xp,xp))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(xp,xp),sz00) ),
    inference(rew,[status(thm),theory(equality)],[15300,16984]),
    [iquote('0:Rew:15300.0,16984.2')] ).

cnf(17111,plain,
    equal(sdtpldt0(xp,xp),sz00),
    inference(ssi,[status(thm)],[17110,2,77,5]),
    [iquote('0:SSi:17110.1,17110.0,2.0,77.0,5.2,5.0')] ).

cnf(17139,plain,
    ( ~ aInteger0(sdtasdt0(xp,u))
    | ~ aInteger0(u)
    | equal(sdtasdt0(xp,u),sdtpldt0(smndt0(u),smndt0(u))) ),
    inference(obv,[status(thm),theory(equality)],[16968]),
    [iquote('0:Obv:16968.0')] ).

cnf(17140,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(xp,u),sdtpldt0(smndt0(u),smndt0(u))) ),
    inference(ssi,[status(thm)],[17139,78,5]),
    [iquote('0:SSi:17139.0,78.0,5.2')] ).

cnf(17142,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,sdtpldt0(smndt0(u),smndt0(u))),smndt0(u)) ),
    inference(rew,[status(thm),theory(equality)],[17140,8512]),
    [iquote('0:Rew:17140.1,8512.1')] ).

cnf(17154,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(xp,sdtasdt0(skc43,u)),sdtpldt0(smndt0(u),smndt0(u))) ),
    inference(rew,[status(thm),theory(equality)],[17140,17026]),
    [iquote('0:Rew:17140.1,17026.1')] ).

cnf(17183,plain,
    ( ~ aInteger0(sdtpldt0(smndt0(sz10),smndt0(sz10)))
    | ~ aInteger0(skc43)
    | equal(sdtpldt0(smndt0(skc43),smndt0(skc43)),xp) ),
    inference(rew,[status(thm),theory(equality)],[16995,16978]),
    [iquote('0:Rew:16995.0,16978.2')] ).

cnf(17184,plain,
    equal(sdtpldt0(smndt0(skc43),smndt0(skc43)),xp),
    inference(ssi,[status(thm)],[17183,6,77,288]),
    [iquote('0:SSi:17183.1,17183.0,6.0,77.0,288.2,288.0')] ).

cnf(17300,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz10)
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(xp,u),sdtpldt0(sz10,sdtpldt0(sz10,u))) ),
    inference(spr,[status(thm),theory(equality)],[17105,169]),
    [iquote('0:SpR:17105.0,169.3')] ).

cnf(17301,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz10)
    | ~ aInteger0(sz10)
    | equal(sdtasdt0(xp,u),sdtpldt0(sdtasdt0(sz10,u),sdtasdt0(sz10,u))) ),
    inference(spr,[status(thm),theory(equality)],[17105,184]),
    [iquote('0:SpR:17105.0,184.3')] ).

cnf(17306,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(xp,u),sdtpldt0(sz10,sdtpldt0(sz10,u))) ),
    inference(obv,[status(thm),theory(equality)],[17300]),
    [iquote('0:Obv:17300.1')] ).

cnf(17307,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(xp,u),sdtpldt0(sz10,sdtpldt0(sz10,u))) ),
    inference(ssi,[status(thm)],[17306,2]),
    [iquote('0:SSi:17306.1,2.0')] ).

cnf(17308,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(sz10),u),sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(sz10,u)))) ),
    inference(rew,[status(thm),theory(equality)],[17307,7711]),
    [iquote('0:Rew:17307.1,7711.1')] ).

cnf(17316,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,smndt0(sz10)),sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(sz10,u)))) ),
    inference(rew,[status(thm),theory(equality)],[17307,15049]),
    [iquote('0:Rew:17307.1,15049.1')] ).

cnf(17320,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(skc43),u),sdtpldt0(skc43,sdtpldt0(sz10,sdtpldt0(sz10,u)))) ),
    inference(rew,[status(thm),theory(equality)],[17307,17014]),
    [iquote('0:Rew:17307.1,17014.1')] ).

cnf(17324,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz10)
    | equal(sdtasdt0(xp,u),sdtpldt0(sdtasdt0(sz10,u),sdtasdt0(sz10,u))) ),
    inference(obv,[status(thm),theory(equality)],[17301]),
    [iquote('0:Obv:17301.1')] ).

cnf(17325,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz10)
    | equal(sdtasdt0(xp,u),sdtpldt0(u,u)) ),
    inference(rew,[status(thm),theory(equality)],[47,17324]),
    [iquote('0:Rew:47.1,17324.2')] ).

cnf(17326,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(u),smndt0(u)),sdtpldt0(u,u)) ),
    inference(rew,[status(thm),theory(equality)],[17140,17325]),
    [iquote('0:Rew:17140.1,17325.2')] ).

cnf(17327,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(u),smndt0(u)),sdtpldt0(u,u)) ),
    inference(ssi,[status(thm)],[17326,2]),
    [iquote('0:SSi:17326.1,2.0')] ).

cnf(17329,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(xp,u),sdtpldt0(u,u)) ),
    inference(rew,[status(thm),theory(equality)],[17327,17140]),
    [iquote('0:Rew:17327.1,17140.1')] ).

cnf(17332,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(u,sdtpldt0(u,u)),smndt0(u)) ),
    inference(rew,[status(thm),theory(equality)],[17327,17142]),
    [iquote('0:Rew:17327.1,17142.1')] ).

cnf(17335,plain,
    ( ~ aInteger0(u)
    | equal(sdtasdt0(xp,sdtasdt0(skc43,u)),sdtpldt0(u,u)) ),
    inference(rew,[status(thm),theory(equality)],[17327,17154]),
    [iquote('0:Rew:17327.1,17154.1')] ).

cnf(17413,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(skc43)
    | equal(sdtpldt0(xp,skc43),smndt0(skc43)) ),
    inference(spr,[status(thm),theory(equality)],[17000,109]),
    [iquote('0:SpR:17000.0,109.2')] ).

cnf(17418,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(xp)
    | ~ aInteger0(skc43)
    | equal(sdtpldt0(smndt0(skc43),u),sdtpldt0(skc43,sdtpldt0(xp,u))) ),
    inference(spr,[status(thm),theory(equality)],[17000,169]),
    [iquote('0:SpR:17000.0,169.3')] ).

cnf(17422,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(skc43)
    | equal(sdtpldt0(sz10,sdtpldt0(sz10,skc43)),smndt0(skc43)) ),
    inference(rew,[status(thm),theory(equality)],[17307,17413]),
    [iquote('0:Rew:17307.1,17413.2')] ).

cnf(17423,plain,
    equal(sdtpldt0(sz10,sdtpldt0(sz10,skc43)),smndt0(skc43)),
    inference(ssi,[status(thm)],[17422,6,5]),
    [iquote('0:SSi:17422.1,17422.0,6.0,5.0')] ).

cnf(17425,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(xp)
    | ~ aInteger0(skc43)
    | equal(sdtpldt0(skc43,sdtpldt0(sz10,sdtpldt0(sz10,u))),sdtpldt0(xp,sdtpldt0(skc43,u))) ),
    inference(rew,[status(thm),theory(equality)],[17320,17418,7740]),
    [iquote('0:Rew:17320.1,17418.3,7740.3,17418.3')] ).

cnf(17426,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(skc43,sdtpldt0(sz10,sdtpldt0(sz10,u))),sdtpldt0(xp,sdtpldt0(skc43,u))) ),
    inference(ssi,[status(thm)],[17425,6,5]),
    [iquote('0:SSi:17425.2,17425.1,6.0,5.0')] ).

cnf(17427,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(skc43),u),sdtpldt0(xp,sdtpldt0(skc43,u))) ),
    inference(rew,[status(thm),theory(equality)],[17426,17320]),
    [iquote('0:Rew:17426.1,17320.1')] ).

cnf(17562,plain,
    ( ~ aInteger0(smndt0(skc43))
    | ~ aInteger0(smndt0(skc43))
    | equal(sdtpldt0(smndt0(smndt0(skc43)),xp),smndt0(skc43)) ),
    inference(spr,[status(thm),theory(equality)],[17184,7735]),
    [iquote('0:SpR:17184.0,7735.2')] ).

cnf(17573,plain,
    ( ~ aInteger0(smndt0(skc43))
    | equal(sdtpldt0(smndt0(smndt0(skc43)),xp),smndt0(skc43)) ),
    inference(obv,[status(thm),theory(equality)],[17562]),
    [iquote('0:Obv:17562.0')] ).

cnf(17574,plain,
    equal(sdtpldt0(smndt0(smndt0(skc43)),xp),smndt0(skc43)),
    inference(ssi,[status(thm)],[17573,29,6]),
    [iquote('0:SSi:17573.0,29.0,6.1')] ).

cnf(17604,plain,
    ( ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(xp,sz10),smndt0(sz10)) ),
    inference(spr,[status(thm),theory(equality)],[17109,44]),
    [iquote('0:SpR:17109.0,44.1')] ).

cnf(17620,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz00)
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtasdt0(sdtpldt0(xp,sz10),u),sdtpldt0(sdtasdt0(smndt0(sz10),u),sdtasdt0(sz00,u))) ),
    inference(spr,[status(thm),theory(equality)],[17109,184]),
    [iquote('0:SpR:17109.0,184.3')] ).

cnf(17624,plain,
    equal(sdtpldt0(xp,sz10),smndt0(sz10)),
    inference(ssi,[status(thm)],[17604,288]),
    [iquote('0:SSi:17604.0,288.0')] ).

cnf(17640,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz00)
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtasdt0(sdtpldt0(xp,sz10),u),sdtpldt0(smndt0(u),sz00)) ),
    inference(rew,[status(thm),theory(equality)],[79,17620,49]),
    [iquote('0:Rew:79.1,17620.3,49.1,17620.3')] ).

cnf(17641,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz00)
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtasdt0(smndt0(sz10),u),sdtpldt0(smndt0(u),sz00)) ),
    inference(rew,[status(thm),theory(equality)],[17624,17640]),
    [iquote('0:Rew:17624.0,17640.3')] ).

cnf(17642,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sz00)
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(smndt0(u),sz00),smndt0(u)) ),
    inference(rew,[status(thm),theory(equality)],[79,17641]),
    [iquote('0:Rew:79.1,17641.3')] ).

cnf(17643,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(u),sz00),smndt0(u)) ),
    inference(ssi,[status(thm)],[17642,288,1]),
    [iquote('0:SSi:17642.2,17642.1,288.0,1.0')] ).

cnf(17750,plain,
    ( ~ aInteger0(smndt0(skc43))
    | equal(sdtpldt0(smndt0(skc43),xp),smndt0(smndt0(skc43))) ),
    inference(spr,[status(thm),theory(equality)],[17184,17332]),
    [iquote('0:SpR:17184.0,17332.1')] ).

cnf(17760,plain,
    equal(sdtpldt0(smndt0(skc43),xp),smndt0(smndt0(skc43))),
    inference(ssi,[status(thm)],[17750,29,6]),
    [iquote('0:SSi:17750.0,29.0,6.1')] ).

cnf(17818,plain,
    ( ~ aInteger0(sdtpldt0(sz10,skc43))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),smndt0(skc43)),sdtpldt0(sz10,skc43)) ),
    inference(spr,[status(thm),theory(equality)],[17423,7735]),
    [iquote('0:SpR:17423.0,7735.2')] ).

cnf(17820,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sdtpldt0(sz10,skc43))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(sz10,skc43),u)),sdtpldt0(smndt0(skc43),u)) ),
    inference(spr,[status(thm),theory(equality)],[17423,169]),
    [iquote('0:SpR:17423.0,169.3')] ).

cnf(17823,plain,
    equal(sdtpldt0(smndt0(sz10),smndt0(skc43)),sdtpldt0(sz10,skc43)),
    inference(ssi,[status(thm)],[17818,2,77,6]),
    [iquote('0:SSi:17818.1,17818.0,2.0,77.0,2.2,6.0')] ).

cnf(17824,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(sdtpldt0(sz10,skc43))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(sz10,skc43),u)),sdtpldt0(xp,sdtpldt0(skc43,u))) ),
    inference(rew,[status(thm),theory(equality)],[17427,17820]),
    [iquote('0:Rew:17427.1,17820.3')] ).

cnf(17825,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(sz10,skc43),u)),sdtpldt0(xp,sdtpldt0(skc43,u))) ),
    inference(ssi,[status(thm)],[17824,2,77,6]),
    [iquote('0:SSi:17824.2,17824.1,2.0,77.0,2.2,6.0')] ).

cnf(17901,plain,
    ( ~ aInteger0(skc43)
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtasdt0(xp,smndt0(skc43)),sdtpldt0(smndt0(sz10),smndt0(sz10))) ),
    inference(spr,[status(thm),theory(equality)],[80,17335]),
    [iquote('0:SpR:80.1,17335.1')] ).

cnf(17911,plain,
    ( ~ aInteger0(skc43)
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtasdt0(xp,smndt0(skc43)),xp) ),
    inference(rew,[status(thm),theory(equality)],[16995,17901]),
    [iquote('0:Rew:16995.0,17901.2')] ).

cnf(17912,plain,
    equal(sdtasdt0(xp,smndt0(skc43)),xp),
    inference(ssi,[status(thm)],[17911,288,6]),
    [iquote('0:SSi:17911.1,17911.0,288.0,6.0')] ).

cnf(17954,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(smndt0(smndt0(skc43)))
    | equal(sdtpldt0(xp,smndt0(smndt0(skc43))),smndt0(skc43)) ),
    inference(spr,[status(thm),theory(equality)],[17574,109]),
    [iquote('0:SpR:17574.0,109.2')] ).

cnf(17963,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(smndt0(smndt0(skc43)))
    | equal(sdtpldt0(sz10,sdtpldt0(sz10,smndt0(smndt0(skc43)))),smndt0(skc43)) ),
    inference(rew,[status(thm),theory(equality)],[17307,17954]),
    [iquote('0:Rew:17307.1,17954.2')] ).

cnf(17964,plain,
    equal(sdtpldt0(sz10,sdtpldt0(sz10,smndt0(smndt0(skc43)))),smndt0(skc43)),
    inference(ssi,[status(thm)],[17963,29,6,5]),
    [iquote('0:SSi:17963.1,17963.0,29.0,29.0,6.1,5.1')] ).

cnf(18074,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(smndt0(skc43))
    | equal(sdtpldt0(xp,smndt0(skc43)),smndt0(smndt0(skc43))) ),
    inference(spr,[status(thm),theory(equality)],[17760,109]),
    [iquote('0:SpR:17760.0,109.2')] ).

cnf(18079,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(xp)
    | ~ aInteger0(smndt0(skc43))
    | equal(sdtpldt0(smndt0(smndt0(skc43)),u),sdtpldt0(smndt0(skc43),sdtpldt0(xp,u))) ),
    inference(spr,[status(thm),theory(equality)],[17760,169]),
    [iquote('0:SpR:17760.0,169.3')] ).

cnf(18085,plain,
    ( ~ aInteger0(xp)
    | ~ aInteger0(smndt0(skc43))
    | equal(sdtpldt0(sz10,sdtpldt0(sz10,smndt0(skc43))),smndt0(smndt0(skc43))) ),
    inference(rew,[status(thm),theory(equality)],[17307,18074]),
    [iquote('0:Rew:17307.1,18074.2')] ).

cnf(18086,plain,
    equal(sdtpldt0(sz10,sdtpldt0(sz10,smndt0(skc43))),smndt0(smndt0(skc43))),
    inference(ssi,[status(thm)],[18085,29,6,5]),
    [iquote('0:SSi:18085.1,18085.0,29.0,6.0,5.1')] ).

cnf(18090,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(xp)
    | ~ aInteger0(smndt0(skc43))
    | equal(sdtpldt0(smndt0(smndt0(skc43)),u),sdtpldt0(xp,sdtpldt0(xp,sdtpldt0(skc43,u)))) ),
    inference(rew,[status(thm),theory(equality)],[17427,18079,7740]),
    [iquote('0:Rew:17427.1,18079.3,7740.3,18079.3')] ).

cnf(18091,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(smndt0(skc43)),u),sdtpldt0(xp,sdtpldt0(xp,sdtpldt0(skc43,u)))) ),
    inference(ssi,[status(thm)],[18090,29,6,5]),
    [iquote('0:SSi:18090.2,18090.1,29.0,6.0,5.1')] ).

cnf(18333,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(skc43))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(sdtpldt0(sz10,skc43),u),sdtpldt0(smndt0(sz10),sdtpldt0(smndt0(skc43),u))) ),
    inference(spr,[status(thm),theory(equality)],[17823,169]),
    [iquote('0:SpR:17823.0,169.3')] ).

cnf(18342,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(skc43))
    | ~ aInteger0(smndt0(sz10))
    | equal(sdtpldt0(sdtpldt0(sz10,skc43),u),sdtpldt0(smndt0(sz10),sdtpldt0(xp,sdtpldt0(skc43,u)))) ),
    inference(rew,[status(thm),theory(equality)],[17427,18333]),
    [iquote('0:Rew:17427.1,18333.3')] ).

cnf(18343,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(sdtpldt0(sz10,skc43),u),sdtpldt0(smndt0(sz10),sdtpldt0(xp,sdtpldt0(skc43,u)))) ),
    inference(ssi,[status(thm)],[18342,288,29,6]),
    [iquote('0:SSi:18342.2,18342.1,288.0,29.1,6.0')] ).

cnf(18344,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(sz10,sdtpldt0(smndt0(sz10),sdtpldt0(xp,sdtpldt0(skc43,u)))),sdtpldt0(xp,sdtpldt0(skc43,u))) ),
    inference(rew,[status(thm),theory(equality)],[18343,17825]),
    [iquote('0:Rew:18343.1,17825.1')] ).

cnf(18573,plain,
    ( ~ aInteger0(sdtpldt0(sz10,smndt0(smndt0(skc43))))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),smndt0(skc43)),sdtpldt0(sz10,smndt0(smndt0(skc43)))) ),
    inference(spr,[status(thm),theory(equality)],[17964,7735]),
    [iquote('0:SpR:17964.0,7735.2')] ).

cnf(18578,plain,
    ( ~ aInteger0(sdtpldt0(sz10,smndt0(smndt0(skc43))))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sz10,smndt0(smndt0(skc43))),sdtpldt0(sz10,skc43)) ),
    inference(rew,[status(thm),theory(equality)],[17823,18573]),
    [iquote('0:Rew:17823.0,18573.2')] ).

cnf(18579,plain,
    equal(sdtpldt0(sz10,smndt0(smndt0(skc43))),sdtpldt0(sz10,skc43)),
    inference(ssi,[status(thm)],[18578,2,77,29,6]),
    [iquote('0:SSi:18578.1,18578.0,2.0,77.1,2.1,29.0,29.2,6.0')] ).

cnf(18591,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(smndt0(skc43)))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sdtpldt0(sz10,skc43),u),sdtpldt0(sz10,sdtpldt0(smndt0(smndt0(skc43)),u))) ),
    inference(spr,[status(thm),theory(equality)],[18579,169]),
    [iquote('0:SpR:18579.0,169.3')] ).

cnf(18601,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(smndt0(skc43)))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),sdtpldt0(xp,sdtpldt0(skc43,u))),sdtpldt0(sz10,sdtpldt0(xp,sdtpldt0(xp,sdtpldt0(skc43,u))))) ),
    inference(rew,[status(thm),theory(equality)],[18343,18591,18091]),
    [iquote('0:Rew:18343.1,18591.3,18091.1,18591.3')] ).

cnf(18602,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(sz10),sdtpldt0(xp,sdtpldt0(skc43,u))),sdtpldt0(sz10,sdtpldt0(xp,sdtpldt0(xp,sdtpldt0(skc43,u))))) ),
    inference(ssi,[status(thm)],[18601,2,29,6]),
    [iquote('0:SSi:18601.2,18601.1,2.0,29.1,29.1,6.0')] ).

cnf(18604,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(xp,sdtpldt0(xp,sdtpldt0(skc43,u))))),sdtpldt0(xp,sdtpldt0(skc43,u))) ),
    inference(rew,[status(thm),theory(equality)],[18602,18344]),
    [iquote('0:Rew:18602.1,18344.1')] ).

cnf(22776,plain,
    ( ~ aInteger0(skc43)
    | ~ aInteger0(sz10)
    | equal(smndt0(sdtpldt0(sz10,skc43)),sdtpldt0(sz10,skc43)) ),
    inference(spr,[status(thm),theory(equality)],[8538,17823]),
    [iquote('0:SpR:8538.2,17823.0')] ).

cnf(22782,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(u),sz10),smndt0(sdtpldt0(u,smndt0(sz10)))) ),
    inference(spr,[status(thm),theory(equality)],[15222,8538]),
    [iquote('0:SpR:15222.0,8538.2')] ).

cnf(22783,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(u))
    | ~ aInteger0(v)
    | equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
    inference(spr,[status(thm),theory(equality)],[15399,8538]),
    [iquote('0:SpR:15399.1,8538.2')] ).

cnf(22786,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(sz10))
    | equal(smndt0(sdtpldt0(smndt0(sz10),u)),sdtpldt0(sz10,smndt0(u))) ),
    inference(spr,[status(thm),theory(equality)],[15222,8538]),
    [iquote('0:SpR:15222.0,8538.2')] ).

cnf(22804,plain,
    equal(smndt0(sdtpldt0(sz10,skc43)),sdtpldt0(sz10,skc43)),
    inference(ssi,[status(thm)],[22776,2,6]),
    [iquote('0:SSi:22776.1,22776.0,2.0,6.0')] ).

cnf(22824,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(u),sz10),smndt0(sdtpldt0(u,smndt0(sz10)))) ),
    inference(ssi,[status(thm)],[22782,288]),
    [iquote('0:SSi:22782.0,288.0')] ).

cnf(22825,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(sz10))
    | equal(smndt0(sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(sz10,u)))),sdtpldt0(sz10,smndt0(u))) ),
    inference(rew,[status(thm),theory(equality)],[17308,22786]),
    [iquote('0:Rew:17308.1,22786.2')] ).

cnf(22826,plain,
    ( ~ aInteger0(u)
    | equal(smndt0(sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(sz10,u)))),sdtpldt0(sz10,smndt0(u))) ),
    inference(ssi,[status(thm)],[22825,288]),
    [iquote('0:SSi:22825.1,288.0')] ).

cnf(22835,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
    inference(ssi,[status(thm)],[22783,29]),
    [iquote('0:SSi:22783.1,29.1')] ).

cnf(22836,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(v)
    | equal(sdtpldt0(v,smndt0(sdtpldt0(v,smndt0(u)))),u) ),
    inference(rew,[status(thm),theory(equality)],[22835,7732]),
    [iquote('0:Rew:22835.2,7732.2')] ).

cnf(23589,plain,
    ( ~ aInteger0(sdtpldt0(sz10,smndt0(skc43)))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(smndt0(smndt0(skc43))))),sz00) ),
    inference(spr,[status(thm),theory(equality)],[18086,7743]),
    [iquote('0:SpR:18086.0,7743.2')] ).

cnf(23627,plain,
    ( ~ aInteger0(skc43)
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sz10,sdtpldt0(skc43,sdtpldt0(sz10,skc43))),sz00) ),
    inference(spr,[status(thm),theory(equality)],[22804,7743]),
    [iquote('0:SpR:22804.0,7743.2')] ).

cnf(23658,plain,
    equal(sdtpldt0(sz10,sdtpldt0(skc43,sdtpldt0(sz10,skc43))),sz00),
    inference(ssi,[status(thm)],[23627,2,6]),
    [iquote('0:SSi:23627.1,23627.0,2.0,6.0')] ).

cnf(23739,plain,
    equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(smndt0(smndt0(skc43))))),sz00),
    inference(ssi,[status(thm)],[23589,2,77,29,6]),
    [iquote('0:SSi:23589.1,23589.0,2.0,77.1,2.0,29.2,6.0')] ).

cnf(24078,plain,
    ( ~ aInteger0(sdtpldt0(skc43,sdtpldt0(sz10,skc43)))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(smndt0(sz10),sz00),sdtpldt0(skc43,sdtpldt0(sz10,skc43))) ),
    inference(spr,[status(thm),theory(equality)],[23658,7735]),
    [iquote('0:SpR:23658.0,7735.2')] ).

cnf(24090,plain,
    ( ~ aInteger0(sdtpldt0(skc43,sdtpldt0(sz10,skc43)))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(skc43,sdtpldt0(sz10,skc43)),smndt0(sz10)) ),
    inference(rew,[status(thm),theory(equality)],[17643,24078]),
    [iquote('0:Rew:17643.1,24078.2')] ).

cnf(24091,plain,
    equal(sdtpldt0(skc43,sdtpldt0(sz10,skc43)),smndt0(sz10)),
    inference(ssi,[status(thm)],[24090,2,77,6]),
    [iquote('0:SSi:24090.1,24090.0,2.0,77.0,6.2,77.0,2.2,6.0')] ).

cnf(24105,plain,
    ( ~ aInteger0(sdtpldt0(sz10,skc43))
    | ~ aInteger0(skc43)
    | equal(sdtpldt0(smndt0(skc43),smndt0(sz10)),sdtpldt0(sz10,skc43)) ),
    inference(spr,[status(thm),theory(equality)],[24091,7735]),
    [iquote('0:SpR:24091.0,7735.2')] ).

cnf(24116,plain,
    equal(sdtpldt0(smndt0(skc43),smndt0(sz10)),sdtpldt0(sz10,skc43)),
    inference(ssi,[status(thm)],[24105,6,77,2]),
    [iquote('0:SSi:24105.1,24105.0,6.0,77.0,2.2,6.0')] ).

cnf(24356,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(smndt0(skc43))
    | equal(sdtpldt0(smndt0(smndt0(skc43)),sdtpldt0(sz10,skc43)),smndt0(sz10)) ),
    inference(spr,[status(thm),theory(equality)],[24116,7735]),
    [iquote('0:SpR:24116.0,7735.2')] ).

cnf(24381,plain,
    equal(sdtpldt0(smndt0(smndt0(skc43)),sdtpldt0(sz10,skc43)),smndt0(sz10)),
    inference(ssi,[status(thm)],[24356,29,6,288]),
    [iquote('0:SSi:24356.1,24356.0,29.0,6.0,288.1')] ).

cnf(24486,plain,
    ( ~ aInteger0(sdtpldt0(sz10,skc43))
    | ~ aInteger0(smndt0(smndt0(skc43)))
    | equal(sdtpldt0(smndt0(smndt0(smndt0(skc43))),smndt0(sz10)),sdtpldt0(sz10,skc43)) ),
    inference(spr,[status(thm),theory(equality)],[24381,7735]),
    [iquote('0:SpR:24381.0,7735.2')] ).

cnf(24495,plain,
    equal(sdtpldt0(smndt0(smndt0(smndt0(skc43))),smndt0(sz10)),sdtpldt0(sz10,skc43)),
    inference(ssi,[status(thm)],[24486,29,6,77,2]),
    [iquote('0:SSi:24486.1,24486.0,29.0,29.0,6.2,77.0,2.1,6.1')] ).

cnf(25233,plain,
    ( ~ aInteger0(sz10)
    | ~ aInteger0(smndt0(smndt0(smndt0(skc43))))
    | equal(sdtpldt0(smndt0(smndt0(smndt0(skc43))),smndt0(sdtpldt0(sz10,skc43))),sz10) ),
    inference(spr,[status(thm),theory(equality)],[24495,22836]),
    [iquote('0:SpR:24495.0,22836.2')] ).

cnf(25251,plain,
    ( ~ aInteger0(sz10)
    | ~ aInteger0(smndt0(smndt0(smndt0(skc43))))
    | equal(sdtpldt0(smndt0(smndt0(smndt0(skc43))),sdtpldt0(sz10,skc43)),sz10) ),
    inference(rew,[status(thm),theory(equality)],[22804,25233]),
    [iquote('0:Rew:22804.0,25233.2')] ).

cnf(25252,plain,
    equal(sdtpldt0(smndt0(smndt0(smndt0(skc43))),sdtpldt0(sz10,skc43)),sz10),
    inference(ssi,[status(thm)],[25251,29,6,2]),
    [iquote('0:SSi:25251.1,25251.0,29.0,29.0,29.1,6.1,2.1')] ).

cnf(25273,plain,
    ( ~ aInteger0(sdtpldt0(sz10,skc43))
    | ~ aInteger0(smndt0(smndt0(smndt0(skc43))))
    | equal(sdtpldt0(smndt0(smndt0(smndt0(smndt0(skc43)))),sz10),sdtpldt0(sz10,skc43)) ),
    inference(spr,[status(thm),theory(equality)],[25252,7735]),
    [iquote('0:SpR:25252.0,7735.2')] ).

cnf(25283,plain,
    ( ~ aInteger0(sdtpldt0(sz10,skc43))
    | ~ aInteger0(smndt0(smndt0(smndt0(skc43))))
    | equal(sdtpldt0(sz10,smndt0(smndt0(smndt0(smndt0(skc43))))),sdtpldt0(sz10,skc43)) ),
    inference(rew,[status(thm),theory(equality)],[22826,25273,17316,22824]),
    [iquote('0:Rew:22826.1,25273.2,17316.1,25273.2,22824.1,25273.2')] ).

cnf(25284,plain,
    equal(sdtpldt0(sz10,smndt0(smndt0(smndt0(smndt0(skc43))))),sdtpldt0(sz10,skc43)),
    inference(ssi,[status(thm)],[25283,29,6,77,2]),
    [iquote('0:SSi:25283.1,25283.0,29.0,29.0,29.2,6.0,77.1,2.1,6.1')] ).

cnf(25871,plain,
    ( ~ aInteger0(smndt0(smndt0(smndt0(skc43))))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sz10,smndt0(sdtpldt0(sz10,skc43))),smndt0(smndt0(smndt0(skc43)))) ),
    inference(spr,[status(thm),theory(equality)],[25284,22836]),
    [iquote('0:SpR:25284.0,22836.2')] ).

cnf(25885,plain,
    ( ~ aInteger0(smndt0(smndt0(smndt0(skc43))))
    | ~ aInteger0(sz10)
    | equal(smndt0(smndt0(smndt0(skc43))),smndt0(skc43)) ),
    inference(rew,[status(thm),theory(equality)],[17423,25871,22804]),
    [iquote('0:Rew:17423.0,25871.2,22804.0,25871.2')] ).

cnf(25886,plain,
    equal(smndt0(smndt0(smndt0(skc43))),smndt0(skc43)),
    inference(ssi,[status(thm)],[25885,2,29,6]),
    [iquote('0:SSi:25885.1,25885.0,2.0,29.1,29.1,29.1,6.0')] ).

cnf(25895,plain,
    equal(sdtpldt0(sz10,sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(skc43))),sz00),
    inference(rew,[status(thm),theory(equality)],[25886,23739]),
    [iquote('0:Rew:25886.0,23739.0')] ).

cnf(27343,plain,
    ( ~ aInteger0(sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(skc43)))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(skc43)),sdtpldt0(smndt0(sz10),sz00)) ),
    inference(spr,[status(thm),theory(equality)],[25895,7735]),
    [iquote('0:SpR:25895.0,7735.2')] ).

cnf(27362,plain,
    ( ~ aInteger0(sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(skc43)))
    | ~ aInteger0(sz10)
    | equal(sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(skc43)),smndt0(sz10)) ),
    inference(rew,[status(thm),theory(equality)],[17643,27343]),
    [iquote('0:Rew:17643.1,27343.2')] ).

cnf(27363,plain,
    equal(sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(skc43)),smndt0(sz10)),
    inference(ssi,[status(thm)],[27362,2,77,29,6]),
    [iquote('0:SSi:27362.1,27362.0,2.0,77.1,77.0,2.1,29.0,6.2,29.2,6.0')] ).

cnf(27383,plain,
    ( ~ aInteger0(skc43)
    | ~ aInteger0(sdtpldt0(sz10,smndt0(skc43)))
    | equal(sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),smndt0(smndt0(sz10))),skc43) ),
    inference(spr,[status(thm),theory(equality)],[27363,22836]),
    [iquote('0:SpR:27363.0,22836.2')] ).

cnf(27391,plain,
    ( ~ aInteger0(skc43)
    | ~ aInteger0(sdtpldt0(sz10,smndt0(skc43)))
    | equal(sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),sz10),skc43) ),
    inference(rew,[status(thm),theory(equality)],[15222,27383]),
    [iquote('0:Rew:15222.0,27383.2')] ).

cnf(27392,plain,
    equal(sdtpldt0(sdtpldt0(sz10,smndt0(skc43)),sz10),skc43),
    inference(ssi,[status(thm)],[27391,77,2,29,6]),
    [iquote('0:SSi:27391.1,27391.0,77.0,2.0,29.1,6.0,6.2')] ).

cnf(27407,plain,
    ( ~ aInteger0(sz10)
    | ~ aInteger0(sdtpldt0(sz10,smndt0(skc43)))
    | equal(sdtpldt0(sz10,sdtpldt0(sz10,smndt0(skc43))),skc43) ),
    inference(spr,[status(thm),theory(equality)],[27392,109]),
    [iquote('0:SpR:27392.0,109.2')] ).

cnf(27424,plain,
    ( ~ aInteger0(sz10)
    | ~ aInteger0(sdtpldt0(sz10,smndt0(skc43)))
    | equal(smndt0(smndt0(skc43)),skc43) ),
    inference(rew,[status(thm),theory(equality)],[18086,27407]),
    [iquote('0:Rew:18086.0,27407.2')] ).

cnf(27425,plain,
    equal(smndt0(smndt0(skc43)),skc43),
    inference(ssi,[status(thm)],[27424,77,2,29,6]),
    [iquote('0:SSi:27424.1,27424.0,77.0,2.0,29.1,6.0,2.2')] ).

cnf(27445,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(xp,sdtpldt0(xp,sdtpldt0(skc43,u))),sdtpldt0(skc43,u)) ),
    inference(rew,[status(thm),theory(equality)],[27425,18091]),
    [iquote('0:Rew:27425.0,18091.1')] ).

cnf(27472,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(xp,sdtpldt0(skc43,u)),sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(skc43,u)))) ),
    inference(rew,[status(thm),theory(equality)],[27445,18604]),
    [iquote('0:Rew:27445.1,18604.1')] ).

cnf(27488,plain,
    ( ~ aInteger0(u)
    | equal(sdtpldt0(smndt0(skc43),u),sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(skc43,u)))) ),
    inference(rew,[status(thm),theory(equality)],[27472,17427]),
    [iquote('0:Rew:27472.1,17427.1')] ).

cnf(47779,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(skc43))
    | ~ aInteger0(xp)
    | ~ equal(sdtpldt0(xp,sdtasdt0(xp,u)),sz00)
    | equal(sdtpldt0(smndt0(skc43),u),sz00)
    | equal(xp,sz00) ),
    inference(spl,[status(thm),theory(equality)],[17912,8636]),
    [iquote('0:SpL:17912.0,8636.3')] ).

cnf(47783,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(skc43)
    | ~ aInteger0(xp)
    | ~ equal(sdtpldt0(xp,sdtasdt0(xp,u)),sz00)
    | equal(sdtpldt0(skc43,u),sz00)
    | equal(xp,sz00) ),
    inference(spl,[status(thm),theory(equality)],[16998,8636]),
    [iquote('0:SpL:16998.0,8636.3')] ).

cnf(47844,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(skc43)
    | ~ aInteger0(xp)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00)
    | equal(sdtpldt0(skc43,u),sz00)
    | equal(xp,sz00) ),
    inference(rew,[status(thm),theory(equality)],[17329,47783]),
    [iquote('0:Rew:17329.1,47783.3')] ).

cnf(47845,plain,
    ( ~ aInteger0(u)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00)
    | equal(sdtpldt0(skc43,u),sz00)
    | equal(xp,sz00) ),
    inference(ssi,[status(thm)],[47844,5,6]),
    [iquote('0:SSi:47844.2,47844.1,5.0,6.0')] ).

cnf(47846,plain,
    ( ~ aInteger0(u)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00)
    | equal(sdtpldt0(skc43,u),sz00) ),
    inference(mrr,[status(thm)],[47845,25]),
    [iquote('0:MRR:47845.3,25.0')] ).

cnf(47860,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(skc43))
    | ~ aInteger0(xp)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00)
    | equal(sdtpldt0(smndt0(skc43),u),sz00)
    | equal(xp,sz00) ),
    inference(rew,[status(thm),theory(equality)],[17329,47779]),
    [iquote('0:Rew:17329.1,47779.3')] ).

cnf(47861,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(skc43))
    | ~ aInteger0(xp)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00)
    | equal(sdtpldt0(sz10,sdtpldt0(sz10,sz00)),sz00)
    | equal(xp,sz00) ),
    inference(rew,[status(thm),theory(equality)],[47846,47860,27488]),
    [iquote('0:Rew:47846.2,47860.4,27488.1,47860.4')] ).

cnf(47862,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(skc43))
    | ~ aInteger0(xp)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00)
    | equal(xp,sz00)
    | equal(xp,sz00) ),
    inference(rew,[status(thm),theory(equality)],[17105,47861,15236]),
    [iquote('0:Rew:17105.0,47861.4,15236.0,47861.4')] ).

cnf(47863,plain,
    ( ~ aInteger0(u)
    | ~ aInteger0(smndt0(skc43))
    | ~ aInteger0(xp)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00)
    | equal(xp,sz00) ),
    inference(obv,[status(thm),theory(equality)],[47862]),
    [iquote('0:Obv:47862.4')] ).

cnf(47864,plain,
    ( ~ aInteger0(u)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00)
    | equal(xp,sz00) ),
    inference(ssi,[status(thm)],[47863,5,29,6]),
    [iquote('0:SSi:47863.2,47863.1,5.0,29.1,6.0')] ).

cnf(47865,plain,
    ( ~ aInteger0(u)
    | ~ equal(sdtpldt0(xp,sdtpldt0(u,u)),sz00) ),
    inference(mrr,[status(thm)],[47864,25]),
    [iquote('0:MRR:47864.2,25.0')] ).

cnf(60223,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(smndt0(sz10))
    | ~ equal(sdtpldt0(xp,sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(sz10,smndt0(sz10))))),sz00) ),
    inference(spl,[status(thm),theory(equality)],[17308,47865]),
    [iquote('0:SpL:17308.1,47865.1')] ).

cnf(60315,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ equal(sdtpldt0(xp,sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(sz10,smndt0(sz10))))),sz00) ),
    inference(obv,[status(thm),theory(equality)],[60223]),
    [iquote('0:Obv:60223.0')] ).

cnf(60316,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ equal(sz00,sz00) ),
    inference(rew,[status(thm),theory(equality)],[17111,60315,17105,15236,15296]),
    [iquote('0:Rew:17111.0,60315.1,17105.0,60315.1,15236.0,60315.1,15296.0,60315.1')] ).

cnf(60317,plain,
    ~ aInteger0(smndt0(sz10)),
    inference(obv,[status(thm),theory(equality)],[60316]),
    [iquote('0:Obv:60316.1')] ).

cnf(60318,plain,
    $false,
    inference(ssi,[status(thm)],[60317,288]),
    [iquote('0:SSi:60317.0,288.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM454+6 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n007.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 : Tue Jul  5 09:13:27 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 77.39/77.57  
% 77.39/77.57  SPASS V 3.9 
% 77.39/77.57  SPASS beiseite: Proof found.
% 77.39/77.57  % SZS status Theorem
% 77.39/77.57  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 77.39/77.57  SPASS derived 35998 clauses, backtracked 3317 clauses, performed 55 splits and kept 15706 clauses.
% 77.39/77.57  SPASS allocated 159883 KBytes.
% 77.39/77.57  SPASS spent	0:1:17.16 on the problem.
% 77.39/77.57  		0:00:00.04 for the input.
% 77.39/77.57  		0:00:00.25 for the FLOTTER CNF translation.
% 77.39/77.57  		0:00:00.65 for inferences.
% 77.39/77.57  		0:00:02.85 for the backtracking.
% 77.39/77.57  		0:1:12.98 for the reduction.
% 77.39/77.57  
% 77.39/77.57  
% 77.39/77.57  Here is a proof with depth 13, length 265 :
% 77.39/77.57  % SZS output start Refutation
% See solution above
% 90.31/90.47  Formulae used in the proof : mIntZero mIntOne m__2171 m__2232 m__ mIntNeg mAddZero mMulOne mMulZero mAddNeg mIntPlus mIntMult mMulMinOne mAddComm mZeroDiv mMulAsso mAddAsso mDistrib
% 90.31/90.47  
%------------------------------------------------------------------------------