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
%------------------------------------------------------------------------------