TSTP Solution File: RNG122+4 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG122+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:41:32 EDT 2022
% Result : Theorem 31.60s 31.82s
% Output : Refutation 38.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 67
% Syntax : Number of clauses : 332 ( 98 unt; 8 nHn; 332 RR)
% Number of literals : 861 ( 0 equ; 538 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 20 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aElement0(sz00),
file('RNG122+4.p',unknown),
[] ).
cnf(2,axiom,
aElement0(sz10),
file('RNG122+4.p',unknown),
[] ).
cnf(3,axiom,
aElement0(xa),
file('RNG122+4.p',unknown),
[] ).
cnf(4,axiom,
aElement0(xb),
file('RNG122+4.p',unknown),
[] ).
cnf(8,axiom,
aSet0(xI),
file('RNG122+4.p',unknown),
[] ).
cnf(9,axiom,
aIdeal0(xI),
file('RNG122+4.p',unknown),
[] ).
cnf(10,axiom,
aElement0(skc61),
file('RNG122+4.p',unknown),
[] ).
cnf(11,axiom,
aElement0(skc60),
file('RNG122+4.p',unknown),
[] ).
cnf(12,axiom,
aElement0(skc59),
file('RNG122+4.p',unknown),
[] ).
cnf(13,axiom,
aElement0(skc58),
file('RNG122+4.p',unknown),
[] ).
cnf(16,axiom,
aElement0(skc69),
file('RNG122+4.p',unknown),
[] ).
cnf(17,axiom,
aElement0(xq),
file('RNG122+4.p',unknown),
[] ).
cnf(18,axiom,
aElement0(xr),
file('RNG122+4.p',unknown),
[] ).
cnf(27,axiom,
aElement0(skf48(u)),
file('RNG122+4.p',unknown),
[] ).
cnf(28,axiom,
aElement0(skf47(u)),
file('RNG122+4.p',unknown),
[] ).
cnf(29,axiom,
aElementOf0(xu,xI),
file('RNG122+4.p',unknown),
[] ).
cnf(31,axiom,
aElementOf0(xb,xI),
file('RNG122+4.p',unknown),
[] ).
cnf(32,axiom,
~ equal(sz00,sz10),
file('RNG122+4.p',unknown),
[] ).
cnf(35,axiom,
aElement0(skf36(u,v)),
file('RNG122+4.p',unknown),
[] ).
cnf(51,axiom,
aElementOf0(skc71,slsdtgt0(xa)),
file('RNG122+4.p',unknown),
[] ).
cnf(52,axiom,
aElementOf0(skc70,slsdtgt0(xb)),
file('RNG122+4.p',unknown),
[] ).
cnf(54,axiom,
aElementOf0(skc73,slsdtgt0(xa)),
file('RNG122+4.p',unknown),
[] ).
cnf(55,axiom,
aElementOf0(skc72,slsdtgt0(xb)),
file('RNG122+4.p',unknown),
[] ).
cnf(57,axiom,
( ~ aIdeal0(u)
| aSet0(u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(60,axiom,
aElementOf0(skf46(u),slsdtgt0(xa)),
file('RNG122+4.p',unknown),
[] ).
cnf(61,axiom,
aElementOf0(skf45(u),slsdtgt0(xb)),
file('RNG122+4.p',unknown),
[] ).
cnf(62,axiom,
equal(sdtasdt0(xa,skc58),sz00),
file('RNG122+4.p',unknown),
[] ).
cnf(63,axiom,
equal(sdtasdt0(xa,skc59),xa),
file('RNG122+4.p',unknown),
[] ).
cnf(64,axiom,
equal(sdtasdt0(xb,skc60),sz00),
file('RNG122+4.p',unknown),
[] ).
cnf(65,axiom,
equal(sdtasdt0(xb,skc61),xb),
file('RNG122+4.p',unknown),
[] ).
cnf(70,axiom,
equal(sdtasdt0(xu,skc69),xa),
file('RNG122+4.p',unknown),
[] ).
cnf(72,axiom,
equal(sdtpldt0(skc73,skc72),xb),
file('RNG122+4.p',unknown),
[] ).
cnf(73,axiom,
( ~ aElement0(u)
| aElement0(smndt0(u)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(75,axiom,
( ~ aElement0(u)
| aIdeal0(slsdtgt0(u)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(80,axiom,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('RNG122+4.p',unknown),
[] ).
cnf(83,axiom,
equal(sdtpldt0(sdtasdt0(xq,xu),xr),xb),
file('RNG122+4.p',unknown),
[] ).
cnf(84,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(85,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(87,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(sz10,u),u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(88,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('RNG122+4.p',unknown),
[] ).
cnf(89,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
file('RNG122+4.p',unknown),
[] ).
cnf(93,axiom,
equal(smndt0(sdtasdt0(xq,xu)),sdtpldt0(skc71,skc70)),
file('RNG122+4.p',unknown),
[] ).
cnf(94,axiom,
~ equal(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),xr),
file('RNG122+4.p',unknown),
[] ).
cnf(95,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('RNG122+4.p',unknown),
[] ).
cnf(96,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('RNG122+4.p',unknown),
[] ).
cnf(97,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG122+4.p',unknown),
[] ).
cnf(107,axiom,
( ~ aElement0(u)
| ~ equal(sdtasdt0(xu,u),xb) ),
file('RNG122+4.p',unknown),
[] ).
cnf(108,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtpldt0(v,u)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(109,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtasdt0(v,u)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(110,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(smndt0(sz10),u),smndt0(u)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(111,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(122,axiom,
( ~ aElementOf0(u,xI)
| equal(sdtpldt0(skf46(u),skf45(u)),u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(123,axiom,
( ~ aElementOf0(u,slsdtgt0(xb))
| equal(sdtasdt0(xb,skf47(u)),u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(124,axiom,
( ~ aElementOf0(u,slsdtgt0(xa))
| equal(sdtasdt0(xa,skf48(u)),u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(127,axiom,
( ~ aElement0(u)
| ~ aElementOf0(v,xI)
| aElementOf0(sdtasdt0(u,v),xI) ),
file('RNG122+4.p',unknown),
[] ).
cnf(128,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(129,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(135,axiom,
( ~ aElement0(u)
| ~ equal(sdtasdt0(xb,u),v)
| aElementOf0(v,slsdtgt0(xb)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(136,axiom,
( ~ aElement0(u)
| ~ equal(sdtasdt0(xa,u),v)
| aElementOf0(v,slsdtgt0(xa)) ),
file('RNG122+4.p',unknown),
[] ).
cnf(144,axiom,
( ~ skP4(u)
| ~ aElement0(v)
| ~ equal(sdtasdt0(u,v),xb)
| skP3(u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(145,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ equal(sdtasdt0(u,v),xa)
| skP4(u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(151,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ doDivides0(v,u)
| equal(sdtasdt0(v,skf36(u,v)),u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(152,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ equal(sdtasdt0(v,u),sz00)
| equal(u,sz00)
| equal(v,sz00) ),
file('RNG122+4.p',unknown),
[] ).
cnf(154,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ equal(sdtasdt0(v,w),u)
| doDivides0(v,u) ),
file('RNG122+4.p',unknown),
[] ).
cnf(165,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('RNG122+4.p',unknown),
[] ).
cnf(166,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('RNG122+4.p',unknown),
[] ).
cnf(170,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
file('RNG122+4.p',unknown),
[] ).
cnf(188,plain,
aElementOf0(sdtpldt0(skc71,skc70),xI),
inference(rew,[status(thm),theory(equality)],[93,80]),
[iquote('0:Rew:93.0,80.0')] ).
cnf(190,plain,
~ equal(sdtpldt0(sdtpldt0(skc71,skc70),xb),xr),
inference(rew,[status(thm),theory(equality)],[93,94]),
[iquote('0:Rew:93.0,94.0')] ).
cnf(221,plain,
( ~ aElement0(xu)
| ~ aElement0(sz00)
| ~ equal(sz00,xb) ),
inference(spl,[status(thm),theory(equality)],[88,107]),
[iquote('0:SpL:88.1,107.1')] ).
cnf(224,plain,
( ~ aElement0(xu)
| ~ equal(sz00,xb) ),
inference(ssi,[status(thm)],[221,1]),
[iquote('0:SSi:221.1,1.0')] ).
cnf(227,plain,
( ~ aElement0(sz00)
| ~ aElement0(smndt0(sz00))
| equal(smndt0(sz00),sz00) ),
inference(spr,[status(thm),theory(equality)],[96,84]),
[iquote('0:SpR:96.1,84.1')] ).
cnf(229,plain,
equal(smndt0(sz00),sz00),
inference(ssi,[status(thm)],[227,73,1]),
[iquote('0:SSi:227.1,227.0,73.0,1.0,1.1')] ).
cnf(253,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(res,[status(thm),theory(equality)],[29,97]),
[iquote('0:Res:29.0,97.1')] ).
cnf(255,plain,
( ~ aSet0(xI)
| aElement0(sdtpldt0(skc71,skc70)) ),
inference(res,[status(thm),theory(equality)],[188,97]),
[iquote('0:Res:188.0,97.1')] ).
cnf(257,plain,
( ~ aSet0(slsdtgt0(xb))
| aElement0(skc72) ),
inference(res,[status(thm),theory(equality)],[55,97]),
[iquote('0:Res:55.0,97.1')] ).
cnf(258,plain,
( ~ aSet0(slsdtgt0(xb))
| aElement0(skc70) ),
inference(res,[status(thm),theory(equality)],[52,97]),
[iquote('0:Res:52.0,97.1')] ).
cnf(263,plain,
( ~ aSet0(slsdtgt0(xb))
| aElement0(skf45(u)) ),
inference(res,[status(thm),theory(equality)],[61,97]),
[iquote('0:Res:61.0,97.1')] ).
cnf(264,plain,
( ~ aSet0(slsdtgt0(xa))
| aElement0(skc73) ),
inference(res,[status(thm),theory(equality)],[54,97]),
[iquote('0:Res:54.0,97.1')] ).
cnf(271,plain,
( ~ aSet0(slsdtgt0(xa))
| aElement0(skf46(u)) ),
inference(res,[status(thm),theory(equality)],[60,97]),
[iquote('0:Res:60.0,97.1')] ).
cnf(274,plain,
aElement0(xu),
inference(ssi,[status(thm)],[253,9,8]),
[iquote('0:SSi:253.0,9.0,8.0')] ).
cnf(275,plain,
~ equal(sz00,xb),
inference(mrr,[status(thm)],[224,274]),
[iquote('0:MRR:224.0,274.0')] ).
cnf(279,plain,
aElement0(skc72),
inference(ssi,[status(thm)],[257,57,75,4]),
[iquote('0:SSi:257.0,57.0,75.1,4.1')] ).
cnf(280,plain,
aElement0(skc70),
inference(ssi,[status(thm)],[258,57,75,4]),
[iquote('0:SSi:258.0,57.0,75.1,4.1')] ).
cnf(283,plain,
aElement0(skc73),
inference(ssi,[status(thm)],[264,57,75,3]),
[iquote('0:SSi:264.0,57.0,75.1,3.1')] ).
cnf(288,plain,
aElement0(sdtpldt0(skc71,skc70)),
inference(ssi,[status(thm)],[255,9,8]),
[iquote('0:SSi:255.0,9.0,8.0')] ).
cnf(289,plain,
aElement0(skf45(u)),
inference(ssi,[status(thm)],[263,57,75,4]),
[iquote('0:SSi:263.0,57.0,75.1,4.1')] ).
cnf(290,plain,
aElement0(skf46(u)),
inference(ssi,[status(thm)],[271,57,75,3]),
[iquote('0:SSi:271.0,57.0,75.1,3.1')] ).
cnf(352,plain,
( ~ aElement0(skf48(u))
| ~ aElement0(xa)
| ~ aElementOf0(u,slsdtgt0(xa))
| aElement0(u) ),
inference(spr,[status(thm),theory(equality)],[124,109]),
[iquote('0:SpR:124.1,109.2')] ).
cnf(353,plain,
( ~ aElementOf0(u,slsdtgt0(xa))
| aElement0(u) ),
inference(ssi,[status(thm)],[352,3,27]),
[iquote('0:SSi:352.1,352.0,3.0,27.0')] ).
cnf(365,plain,
( ~ aElement0(skf47(u))
| ~ aElement0(xb)
| ~ aElementOf0(u,slsdtgt0(xb))
| aElement0(u) ),
inference(spr,[status(thm),theory(equality)],[123,109]),
[iquote('0:SpR:123.1,109.2')] ).
cnf(366,plain,
( ~ aElementOf0(u,slsdtgt0(xb))
| aElement0(u) ),
inference(ssi,[status(thm)],[365,4,28]),
[iquote('0:SSi:365.1,365.0,4.0,28.0')] ).
cnf(381,plain,
( ~ aElement0(skf45(u))
| ~ aElement0(skf46(u))
| ~ aElementOf0(u,xI)
| aElement0(u) ),
inference(spr,[status(thm),theory(equality)],[122,108]),
[iquote('0:SpR:122.1,108.2')] ).
cnf(383,plain,
( ~ aElementOf0(u,xI)
| aElement0(u) ),
inference(ssi,[status(thm)],[381,290,289]),
[iquote('0:SSi:381.1,381.0,290.0,289.0')] ).
cnf(485,plain,
( ~ aElement0(skc59)
| ~ equal(xa,u)
| aElementOf0(u,slsdtgt0(xa)) ),
inference(spl,[status(thm),theory(equality)],[63,136]),
[iquote('0:SpL:63.0,136.1')] ).
cnf(493,plain,
( ~ equal(xa,u)
| aElementOf0(u,slsdtgt0(xa)) ),
inference(ssi,[status(thm)],[485,12]),
[iquote('0:SSi:485.0,12.0')] ).
cnf(500,plain,
( ~ equal(xa,u)
| aElement0(u) ),
inference(res,[status(thm),theory(equality)],[493,353]),
[iquote('0:Res:493.1,353.0')] ).
cnf(505,plain,
( ~ aElement0(skc61)
| ~ equal(xb,u)
| aElementOf0(u,slsdtgt0(xb)) ),
inference(spl,[status(thm),theory(equality)],[65,135]),
[iquote('0:SpL:65.0,135.1')] ).
cnf(513,plain,
( ~ equal(xb,u)
| aElementOf0(u,slsdtgt0(xb)) ),
inference(ssi,[status(thm)],[505,10]),
[iquote('0:SSi:505.0,10.0')] ).
cnf(520,plain,
( ~ equal(xb,u)
| aElement0(u) ),
inference(res,[status(thm),theory(equality)],[513,366]),
[iquote('0:Res:513.1,366.0')] ).
cnf(591,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(v)
| ~ aElementOf0(u,xI)
| aElementOf0(sdtasdt0(u,v),xI) ),
inference(spr,[status(thm),theory(equality)],[129,127]),
[iquote('0:SpR:129.2,127.2')] ).
cnf(645,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElementOf0(u,xI)
| aElementOf0(sdtasdt0(u,v),xI) ),
inference(obv,[status(thm),theory(equality)],[591]),
[iquote('0:Obv:591.1')] ).
cnf(646,plain,
( ~ aElement0(u)
| ~ aElementOf0(v,xI)
| aElementOf0(sdtasdt0(v,u),xI) ),
inference(mrr,[status(thm)],[645,383]),
[iquote('0:MRR:645.0,383.1')] ).
cnf(677,plain,
( ~ aElement0(xr)
| ~ aElement0(sdtasdt0(xq,xu))
| equal(sdtpldt0(xr,sdtasdt0(xq,xu)),xb) ),
inference(spr,[status(thm),theory(equality)],[128,83]),
[iquote('0:SpR:128.2,83.0')] ).
cnf(704,plain,
( ~ aElement0(xb)
| ~ aElement0(sdtpldt0(skc71,skc70))
| ~ equal(sdtpldt0(xb,sdtpldt0(skc71,skc70)),xr) ),
inference(spl,[status(thm),theory(equality)],[128,190]),
[iquote('0:SpL:128.2,190.0')] ).
cnf(717,plain,
equal(sdtpldt0(xr,sdtasdt0(xq,xu)),xb),
inference(ssi,[status(thm)],[677,109,17,274,18]),
[iquote('0:SSi:677.1,677.0,109.0,17.0,274.0,18.2')] ).
cnf(723,plain,
~ equal(sdtpldt0(xb,sdtpldt0(skc71,skc70)),xr),
inference(ssi,[status(thm)],[704,288,4]),
[iquote('0:SSi:704.1,704.0,288.0,4.0')] ).
cnf(755,plain,
( ~ skP4(xb)
| ~ aElement0(skc61)
| ~ equal(xb,xb)
| skP3(xb) ),
inference(spl,[status(thm),theory(equality)],[65,144]),
[iquote('0:SpL:65.0,144.2')] ).
cnf(765,plain,
( ~ aElement0(u)
| ~ skP4(sz10)
| ~ aElement0(u)
| ~ equal(u,xb)
| skP3(sz10) ),
inference(spl,[status(thm),theory(equality)],[87,144]),
[iquote('0:SpL:87.1,144.2')] ).
cnf(773,plain,
( ~ skP4(xb)
| ~ aElement0(skc61)
| skP3(xb) ),
inference(obv,[status(thm),theory(equality)],[755]),
[iquote('0:Obv:755.2')] ).
cnf(774,plain,
( ~ skP4(xb)
| skP3(xb) ),
inference(ssi,[status(thm)],[773,10]),
[iquote('0:SSi:773.1,10.0')] ).
cnf(778,plain,
( ~ skP4(sz10)
| ~ aElement0(u)
| ~ equal(u,xb)
| skP3(sz10) ),
inference(obv,[status(thm),theory(equality)],[765]),
[iquote('0:Obv:765.0')] ).
cnf(779,plain,
( ~ skP4(sz10)
| ~ equal(u,xb)
| skP3(sz10) ),
inference(mrr,[status(thm)],[778,520]),
[iquote('0:MRR:778.1,520.1')] ).
cnf(794,plain,
( ~ aElement0(xu)
| ~ aElement0(skc69)
| ~ equal(xa,xa)
| skP4(xu) ),
inference(spl,[status(thm),theory(equality)],[70,145]),
[iquote('0:SpL:70.0,145.2')] ).
cnf(795,plain,
( ~ aElement0(xb)
| ~ aElement0(skc60)
| ~ equal(sz00,xa)
| skP4(xb) ),
inference(spl,[status(thm),theory(equality)],[64,145]),
[iquote('0:SpL:64.0,145.2')] ).
cnf(800,plain,
( ~ aElement0(xa)
| ~ aElement0(skc59)
| ~ equal(xa,xa)
| skP4(xa) ),
inference(spl,[status(thm),theory(equality)],[63,145]),
[iquote('0:SpL:63.0,145.2')] ).
cnf(806,plain,
( ~ aElement0(u)
| ~ aElement0(sz10)
| ~ aElement0(u)
| ~ equal(u,xa)
| skP4(sz10) ),
inference(spl,[status(thm),theory(equality)],[87,145]),
[iquote('0:SpL:87.1,145.2')] ).
cnf(807,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| ~ equal(smndt0(u),xa)
| skP4(smndt0(sz10)) ),
inference(spl,[status(thm),theory(equality)],[110,145]),
[iquote('0:SpL:110.1,145.2')] ).
cnf(814,plain,
( ~ aElement0(xu)
| ~ aElement0(skc69)
| skP4(xu) ),
inference(obv,[status(thm),theory(equality)],[794]),
[iquote('0:Obv:794.2')] ).
cnf(815,plain,
skP4(xu),
inference(ssi,[status(thm)],[814,16,274]),
[iquote('0:SSi:814.1,814.0,16.0,274.0')] ).
cnf(816,plain,
( ~ equal(sz00,xa)
| skP4(xb) ),
inference(ssi,[status(thm)],[795,11,4]),
[iquote('0:SSi:795.1,795.0,11.0,4.0')] ).
cnf(818,plain,
( ~ aElement0(xa)
| ~ aElement0(skc59)
| skP4(xa) ),
inference(obv,[status(thm),theory(equality)],[800]),
[iquote('0:Obv:800.2')] ).
cnf(819,plain,
skP4(xa),
inference(ssi,[status(thm)],[818,12,3]),
[iquote('0:SSi:818.1,818.0,12.0,3.0')] ).
cnf(828,plain,
( ~ aElement0(sz10)
| ~ aElement0(u)
| ~ equal(u,xa)
| skP4(sz10) ),
inference(obv,[status(thm),theory(equality)],[806]),
[iquote('0:Obv:806.0')] ).
cnf(829,plain,
( ~ aElement0(u)
| ~ equal(u,xa)
| skP4(sz10) ),
inference(ssi,[status(thm)],[828,2]),
[iquote('0:SSi:828.0,2.0')] ).
cnf(830,plain,
( ~ equal(u,xa)
| skP4(sz10) ),
inference(mrr,[status(thm)],[829,500]),
[iquote('0:MRR:829.0,500.1')] ).
cnf(840,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| ~ equal(smndt0(u),xa)
| skP4(smndt0(sz10)) ),
inference(obv,[status(thm),theory(equality)],[807]),
[iquote('0:Obv:807.0')] ).
cnf(841,plain,
( ~ aElement0(u)
| ~ equal(smndt0(u),xa)
| skP4(smndt0(sz10)) ),
inference(ssi,[status(thm)],[840,73,2]),
[iquote('0:SSi:840.0,73.0,2.1')] ).
cnf(845,plain,
( ~ equal(sz00,xa)
| skP3(xb) ),
inference(sor,[status(thm)],[774,816]),
[iquote('0:SoR:774.0,816.1')] ).
cnf(849,plain,
skP4(sz10),
inference(eqr,[status(thm),theory(equality)],[830]),
[iquote('0:EqR:830.0')] ).
cnf(852,plain,
( ~ equal(u,xb)
| skP3(sz10) ),
inference(mrr,[status(thm)],[779,849]),
[iquote('0:MRR:779.0,849.0')] ).
cnf(853,plain,
skP3(sz10),
inference(aed,[status(thm),theory(equality)],[32,852]),
[iquote('0:AED:32.0,852.0')] ).
cnf(1112,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(skf36(u,smndt0(sz10)))
| ~ doDivides0(smndt0(sz10),u)
| equal(smndt0(skf36(u,smndt0(sz10))),u) ),
inference(spr,[status(thm),theory(equality)],[151,110]),
[iquote('0:SpR:151.3,110.1')] ).
cnf(1126,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(v)
| ~ aElement0(skf36(u,v))
| ~ doDivides0(v,u)
| ~ equal(u,xa)
| skP4(v) ),
inference(spl,[status(thm),theory(equality)],[151,145]),
[iquote('0:SpL:151.3,145.2')] ).
cnf(1136,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(skf36(u,v))
| ~ doDivides0(v,u)
| ~ equal(u,xa)
| skP4(v) ),
inference(obv,[status(thm),theory(equality)],[1126]),
[iquote('0:Obv:1126.1')] ).
cnf(1137,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ doDivides0(v,u)
| ~ equal(u,xa)
| skP4(v) ),
inference(ssi,[status(thm)],[1136,35]),
[iquote('0:SSi:1136.2,35.0')] ).
cnf(1138,plain,
( ~ aElement0(u)
| ~ doDivides0(u,v)
| ~ equal(v,xa)
| skP4(u) ),
inference(mrr,[status(thm)],[1137,500]),
[iquote('0:MRR:1137.0,500.1')] ).
cnf(1142,plain,
( ~ aElement0(u)
| ~ doDivides0(smndt0(sz10),u)
| equal(smndt0(skf36(u,smndt0(sz10))),u) ),
inference(ssi,[status(thm)],[1112,35,73,2,849,853]),
[iquote('0:SSi:1112.2,1112.1,35.0,73.0,2.0,849.1,853.0,73.0,2.0,849.1,853.0')] ).
cnf(1177,plain,
( ~ aElement0(skc60)
| ~ aElement0(xb)
| ~ equal(sz00,sz00)
| equal(sz00,skc60)
| equal(sz00,xb) ),
inference(spl,[status(thm),theory(equality)],[64,152]),
[iquote('0:SpL:64.0,152.2')] ).
cnf(1181,plain,
( ~ aElement0(skc58)
| ~ aElement0(xa)
| ~ equal(sz00,sz00)
| equal(sz00,skc58)
| equal(sz00,xa) ),
inference(spl,[status(thm),theory(equality)],[62,152]),
[iquote('0:SpL:62.0,152.2')] ).
cnf(1204,plain,
( ~ aElement0(skc60)
| ~ aElement0(xb)
| equal(sz00,skc60)
| equal(sz00,xb) ),
inference(obv,[status(thm),theory(equality)],[1177]),
[iquote('0:Obv:1177.2')] ).
cnf(1205,plain,
( equal(sz00,skc60)
| equal(sz00,xb) ),
inference(ssi,[status(thm)],[1204,4,11]),
[iquote('0:SSi:1204.1,1204.0,4.0,11.0')] ).
cnf(1206,plain,
equal(sz00,skc60),
inference(mrr,[status(thm)],[1205,275]),
[iquote('0:MRR:1205.1,275.0')] ).
cnf(1216,plain,
( ~ aElement0(u)
| equal(sdtasdt0(skc60,u),skc60) ),
inference(rew,[status(thm),theory(equality)],[1206,89]),
[iquote('0:Rew:1206.0,89.1')] ).
cnf(1217,plain,
( ~ aElement0(u)
| equal(sdtasdt0(u,skc60),skc60) ),
inference(rew,[status(thm),theory(equality)],[1206,88]),
[iquote('0:Rew:1206.0,88.1')] ).
cnf(1218,plain,
( ~ aElement0(u)
| equal(sdtpldt0(skc60,u),u) ),
inference(rew,[status(thm),theory(equality)],[1206,85]),
[iquote('0:Rew:1206.0,85.1')] ).
cnf(1219,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,skc60),u) ),
inference(rew,[status(thm),theory(equality)],[1206,84]),
[iquote('0:Rew:1206.0,84.1')] ).
cnf(1221,plain,
equal(smndt0(skc60),skc60),
inference(rew,[status(thm),theory(equality)],[1206,229]),
[iquote('0:Rew:1206.0,229.0')] ).
cnf(1229,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,smndt0(u)),skc60) ),
inference(rew,[status(thm),theory(equality)],[1206,95]),
[iquote('0:Rew:1206.0,95.1')] ).
cnf(1243,plain,
( ~ equal(skc60,xa)
| skP3(xb) ),
inference(rew,[status(thm),theory(equality)],[1206,845]),
[iquote('0:Rew:1206.0,845.0')] ).
cnf(1244,plain,
( ~ equal(skc60,xa)
| skP4(xb) ),
inference(rew,[status(thm),theory(equality)],[1206,816]),
[iquote('0:Rew:1206.0,816.0')] ).
cnf(1281,plain,
( ~ aElement0(skc58)
| ~ aElement0(xa)
| equal(sz00,skc58)
| equal(sz00,xa) ),
inference(obv,[status(thm),theory(equality)],[1181]),
[iquote('0:Obv:1181.2')] ).
cnf(1282,plain,
( ~ aElement0(skc58)
| ~ aElement0(xa)
| equal(skc60,skc58)
| equal(skc60,xa) ),
inference(rew,[status(thm),theory(equality)],[1206,1281]),
[iquote('0:Rew:1206.0,1281.3,1206.0,1281.2')] ).
cnf(1283,plain,
( equal(skc60,skc58)
| equal(skc60,xa) ),
inference(ssi,[status(thm)],[1282,3,819,13]),
[iquote('0:SSi:1282.1,1282.0,3.0,819.0,13.0')] ).
cnf(1382,plain,
equal(skc60,skc58),
inference(spt,[spt(split,[position(s1)])],[1283]),
[iquote('1:Spt:1283.0')] ).
cnf(1420,plain,
( ~ aElement0(u)
| equal(sdtasdt0(u,skc58),skc58) ),
inference(rew,[status(thm),theory(equality)],[1382,1217]),
[iquote('1:Rew:1382.0,1217.1')] ).
cnf(1421,plain,
( ~ aElement0(u)
| equal(sdtpldt0(skc58,u),u) ),
inference(rew,[status(thm),theory(equality)],[1382,1218]),
[iquote('1:Rew:1382.0,1218.1')] ).
cnf(1422,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,skc58),u) ),
inference(rew,[status(thm),theory(equality)],[1382,1219]),
[iquote('1:Rew:1382.0,1219.1')] ).
cnf(1426,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,smndt0(u)),skc58) ),
inference(rew,[status(thm),theory(equality)],[1382,1229]),
[iquote('1:Rew:1382.0,1229.1')] ).
cnf(2764,plain,
( ~ aElement0(sdtasdt0(u,v))
| ~ aElement0(u)
| ~ aElement0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[154]),
[iquote('0:EqR:154.3')] ).
cnf(2787,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ aElement0(v)
| ~ aElement0(skf36(u,v))
| ~ doDivides0(v,u)
| ~ equal(u,w)
| doDivides0(v,w) ),
inference(spl,[status(thm),theory(equality)],[151,154]),
[iquote('0:SpL:151.3,154.3')] ).
cnf(2788,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[2764,109]),
[iquote('0:SSi:2764.0,109.2')] ).
cnf(2826,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ aElement0(skf36(u,w))
| ~ doDivides0(w,u)
| ~ equal(u,v)
| doDivides0(w,v) ),
inference(obv,[status(thm),theory(equality)],[2787]),
[iquote('0:Obv:2787.1')] ).
cnf(2827,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ doDivides0(w,u)
| ~ equal(u,v)
| doDivides0(w,v) ),
inference(ssi,[status(thm)],[2826,35]),
[iquote('0:SSi:2826.3,35.0')] ).
cnf(2976,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ aElement0(sdtpldt0(w,v))
| ~ aElement0(u)
| equal(sdtpldt0(u,sdtpldt0(w,v)),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(spr,[status(thm),theory(equality)],[166,128]),
[iquote('0:SpR:166.3,128.2')] ).
cnf(2986,plain,
( ~ aElement0(u)
| ~ aElement0(xr)
| ~ aElement0(sdtasdt0(xq,xu))
| equal(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(xr,u)),sdtpldt0(xb,u)) ),
inference(spr,[status(thm),theory(equality)],[83,166]),
[iquote('0:SpR:83.0,166.3')] ).
cnf(2998,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ aElement0(v)
| ~ aElement0(u)
| equal(sdtpldt0(sdtpldt0(v,u),w),sdtpldt0(u,sdtpldt0(v,w))) ),
inference(spr,[status(thm),theory(equality)],[128,166]),
[iquote('0:SpR:128.2,166.3')] ).
cnf(3054,plain,
( ~ aElement0(u)
| equal(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(xr,u)),sdtpldt0(xb,u)) ),
inference(ssi,[status(thm)],[2986,109,17,274,815,18]),
[iquote('0:SSi:2986.2,2986.1,109.0,17.0,274.0,815.0,18.2')] ).
cnf(3073,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(v,w),u),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[2998]),
[iquote('0:Obv:2998.1')] ).
cnf(3074,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(v,sdtpldt0(w,u)),sdtpldt0(w,sdtpldt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[166,3073]),
[iquote('0:Rew:166.3,3073.3')] ).
cnf(3087,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sdtpldt0(v,u))
| ~ aElement0(w)
| equal(sdtpldt0(w,sdtpldt0(v,u)),sdtpldt0(v,sdtpldt0(u,w))) ),
inference(obv,[status(thm),theory(equality)],[2976]),
[iquote('0:Obv:2976.0')] ).
cnf(3088,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(w,sdtpldt0(v,u)),sdtpldt0(v,sdtpldt0(u,w))) ),
inference(ssi,[status(thm)],[3087,108]),
[iquote('0:SSi:3087.2,108.2')] ).
cnf(3111,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sdtasdt0(v,u))
| equal(sdtasdt0(v,sdtasdt0(u,smndt0(sz10))),smndt0(sdtasdt0(v,u))) ),
inference(spr,[status(thm),theory(equality)],[165,111]),
[iquote('0:SpR:165.3,111.1')] ).
cnf(3134,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(u)
| ~ aElement0(smndt0(sz10))
| equal(sdtasdt0(smndt0(u),v),sdtasdt0(smndt0(sz10),sdtasdt0(u,v))) ),
inference(spr,[status(thm),theory(equality)],[110,165]),
[iquote('0:SpR:110.1,165.3')] ).
cnf(3139,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| equal(sdtasdt0(smndt0(u),v),sdtasdt0(u,sdtasdt0(smndt0(sz10),v))) ),
inference(spr,[status(thm),theory(equality)],[111,165]),
[iquote('0:SpR:111.1,165.3')] ).
cnf(3176,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(v)
| equal(sdtasdt0(smndt0(v),u),sdtasdt0(v,sdtasdt0(smndt0(sz10),u))) ),
inference(obv,[status(thm),theory(equality)],[3139]),
[iquote('0:Obv:3139.0')] ).
cnf(3177,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(v)
| equal(sdtasdt0(smndt0(v),u),sdtasdt0(v,smndt0(u))) ),
inference(rew,[status(thm),theory(equality)],[110,3176]),
[iquote('0:Rew:110.1,3176.3')] ).
cnf(3178,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(smndt0(v),u),sdtasdt0(v,smndt0(u))) ),
inference(ssi,[status(thm)],[3177,73,2,849,853]),
[iquote('0:SSi:3177.1,73.0,2.0,849.0,853.1')] ).
cnf(3179,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(sz10))
| equal(sdtasdt0(smndt0(v),u),sdtasdt0(smndt0(sz10),sdtasdt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[3134]),
[iquote('0:Obv:3134.0')] ).
cnf(3180,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(sz10))
| equal(sdtasdt0(v,smndt0(u)),sdtasdt0(smndt0(sz10),sdtasdt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[3178,3179]),
[iquote('0:Rew:3178.2,3179.3')] ).
cnf(3181,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(v,smndt0(u)),sdtasdt0(smndt0(sz10),sdtasdt0(v,u))) ),
inference(ssi,[status(thm)],[3180,73,2,849,853]),
[iquote('0:SSi:3180.2,73.0,2.0,849.0,853.1')] ).
cnf(3193,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sdtasdt0(v,u))
| equal(sdtasdt0(v,smndt0(u)),smndt0(sdtasdt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[111,3111]),
[iquote('0:Rew:111.1,3111.4')] ).
cnf(3194,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(v,smndt0(u)),smndt0(sdtasdt0(v,u))) ),
inference(ssi,[status(thm)],[3193,109,73,2,849,853]),
[iquote('0:SSi:3193.3,3193.0,109.0,73.0,2.0,849.1,853.2')] ).
cnf(3196,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(smndt0(sz10),sdtasdt0(v,u)),smndt0(sdtasdt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[3194,3181]),
[iquote('0:Rew:3194.2,3181.2')] ).
cnf(3741,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtpldt0(v,u))
| equal(sdtpldt0(sdtasdt0(smndt0(sz10),v),sdtasdt0(smndt0(sz10),u)),smndt0(sdtpldt0(v,u))) ),
inference(spr,[status(thm),theory(equality)],[170,110]),
[iquote('0:SpR:170.3,110.1')] ).
cnf(3862,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtpldt0(v,u))
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[110,3741]),
[iquote('0:Rew:110.1,3741.4,110.1,3741.4')] ).
cnf(4033,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| doDivides0(smndt0(sz10),smndt0(u)) ),
inference(spr,[status(thm),theory(equality)],[110,2788]),
[iquote('0:SpR:110.1,2788.2')] ).
cnf(4034,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(v)
| ~ aElement0(u)
| doDivides0(v,sdtasdt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[129,2788]),
[iquote('0:SpR:129.2,2788.2')] ).
cnf(4070,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| doDivides0(smndt0(sz10),smndt0(u)) ),
inference(obv,[status(thm),theory(equality)],[4033]),
[iquote('0:Obv:4033.0')] ).
cnf(4072,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| doDivides0(u,sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[4034]),
[iquote('0:Obv:4034.1')] ).
cnf(4997,plain,
( ~ aElement0(skf47(u))
| ~ aElementOf0(u,slsdtgt0(xb))
| ~ aElementOf0(xb,xI)
| aElementOf0(u,xI) ),
inference(spr,[status(thm),theory(equality)],[123,646]),
[iquote('0:SpR:123.1,646.2')] ).
cnf(5040,plain,
( ~ aElementOf0(u,slsdtgt0(xb))
| ~ aElementOf0(xb,xI)
| aElementOf0(u,xI) ),
inference(ssi,[status(thm)],[4997,28]),
[iquote('0:SSi:4997.0,28.0')] ).
cnf(5041,plain,
( ~ aElementOf0(u,slsdtgt0(xb))
| aElementOf0(u,xI) ),
inference(mrr,[status(thm)],[5040,31]),
[iquote('0:MRR:5040.1,31.0')] ).
cnf(5182,plain,
aElementOf0(skc70,xI),
inference(res,[status(thm),theory(equality)],[52,5041]),
[iquote('0:Res:52.0,5041.0')] ).
cnf(7650,plain,
( ~ aElement0(u)
| doDivides0(smndt0(sz10),smndt0(u)) ),
inference(ssi,[status(thm)],[4070,73,2,849,853]),
[iquote('0:SSi:4070.0,73.0,2.0,849.0,853.1')] ).
cnf(7722,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(ssi,[status(thm)],[3862,108,73,2,849,853]),
[iquote('0:SSi:3862.3,3862.2,108.0,73.0,2.0,849.1,853.2')] ).
cnf(7957,plain,
( ~ aElement0(skc69)
| ~ aElement0(xu)
| doDivides0(skc69,xa) ),
inference(spr,[status(thm),theory(equality)],[70,4072]),
[iquote('0:SpR:70.0,4072.2')] ).
cnf(7970,plain,
doDivides0(skc69,xa),
inference(ssi,[status(thm)],[7957,274,815,16]),
[iquote('0:SSi:7957.1,7957.0,274.0,815.0,16.0')] ).
cnf(7992,plain,
( ~ aElement0(u)
| ~ aElement0(skc72)
| ~ aElement0(skc73)
| equal(sdtpldt0(skc73,sdtpldt0(skc72,u)),sdtpldt0(xb,u)) ),
inference(spr,[status(thm),theory(equality)],[72,166]),
[iquote('0:SpR:72.0,166.3')] ).
cnf(7996,plain,
( ~ aElement0(u)
| ~ aElement0(skc72)
| ~ aElement0(skc73)
| equal(sdtpldt0(skc72,sdtpldt0(skc73,u)),sdtpldt0(xb,u)) ),
inference(rew,[status(thm),theory(equality)],[3074,7992]),
[iquote('0:Rew:3074.3,7992.3')] ).
cnf(7997,plain,
( ~ aElement0(u)
| equal(sdtpldt0(skc72,sdtpldt0(skc73,u)),sdtpldt0(xb,u)) ),
inference(ssi,[status(thm)],[7996,283,279]),
[iquote('0:SSi:7996.2,7996.1,283.0,279.0')] ).
cnf(8351,plain,
( ~ aElement0(u)
| ~ aElement0(skc58)
| ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,skc58)),sdtasdt0(v,u)) ),
inference(spr,[status(thm),theory(equality)],[1422,170]),
[iquote('1:SpR:1422.1,170.3')] ).
cnf(8367,plain,
( ~ aElement0(skc58)
| ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,skc58)),sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[8351]),
[iquote('1:Obv:8351.0')] ).
cnf(8368,plain,
( ~ aElement0(skc58)
| ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),skc58),sdtasdt0(v,u)) ),
inference(rew,[status(thm),theory(equality)],[1420,8367]),
[iquote('1:Rew:1420.1,8367.3')] ).
cnf(8369,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),skc58),sdtasdt0(v,u)) ),
inference(ssi,[status(thm)],[8368,13]),
[iquote('1:SSi:8368.0,13.0')] ).
cnf(8514,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(u))
| ~ aElement0(u)
| equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(skc58,v)) ),
inference(spr,[status(thm),theory(equality)],[1426,166]),
[iquote('1:SpR:1426.1,166.3')] ).
cnf(8524,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(skc58,u)) ),
inference(obv,[status(thm),theory(equality)],[8514]),
[iquote('1:Obv:8514.0')] ).
cnf(8525,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[1421,8524]),
[iquote('1:Rew:1421.1,8524.3')] ).
cnf(8526,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[8525,73]),
[iquote('1:SSi:8525.1,73.1')] ).
cnf(8804,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ aElement0(sdtasdt0(w,v))
| ~ aElement0(u)
| ~ equal(sdtasdt0(w,sdtasdt0(v,u)),xa)
| skP4(sdtasdt0(w,v)) ),
inference(spl,[status(thm),theory(equality)],[165,145]),
[iquote('0:SpL:165.3,145.2')] ).
cnf(8832,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sdtasdt0(v,u))
| ~ aElement0(w)
| ~ equal(sdtasdt0(v,sdtasdt0(u,w)),xa)
| skP4(sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[8804]),
[iquote('0:Obv:8804.0')] ).
cnf(8833,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| ~ equal(sdtasdt0(v,sdtasdt0(u,w)),xa)
| skP4(sdtasdt0(v,u)) ),
inference(ssi,[status(thm)],[8832,109]),
[iquote('0:SSi:8832.2,109.2')] ).
cnf(12768,plain,
( ~ aElement0(skc69)
| ~ equal(xa,xa)
| skP4(skc69) ),
inference(res,[status(thm),theory(equality)],[7970,1138]),
[iquote('0:Res:7970.0,1138.1')] ).
cnf(12849,plain,
( ~ aElement0(skc69)
| skP4(skc69) ),
inference(obv,[status(thm),theory(equality)],[12768]),
[iquote('0:Obv:12768.1')] ).
cnf(12850,plain,
skP4(skc69),
inference(ssi,[status(thm)],[12849,16]),
[iquote('0:SSi:12849.0,16.0')] ).
cnf(12908,plain,
( ~ aElement0(xr)
| ~ aElement0(smndt0(xr))
| equal(sdtpldt0(sdtasdt0(xq,xu),skc58),sdtpldt0(xb,smndt0(xr))) ),
inference(spr,[status(thm),theory(equality)],[1426,3054]),
[iquote('1:SpR:1426.1,3054.1')] ).
cnf(12917,plain,
equal(sdtpldt0(sdtasdt0(xq,xu),skc58),sdtpldt0(xb,smndt0(xr))),
inference(ssi,[status(thm)],[12908,73,18]),
[iquote('1:SSi:12908.1,12908.0,73.0,18.0,18.1')] ).
cnf(13879,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(smndt0(smndt0(u)))
| ~ aElement0(u)
| equal(sdtpldt0(u,skc58),smndt0(smndt0(u))) ),
inference(spr,[status(thm),theory(equality)],[1426,8526]),
[iquote('1:SpR:1426.1,8526.2')] ).
cnf(13887,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(smndt0(smndt0(u)))
| ~ aElement0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(rew,[status(thm),theory(equality)],[1422,13879]),
[iquote('1:Rew:1422.1,13879.3')] ).
cnf(13888,plain,
( ~ aElement0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(ssi,[status(thm)],[13887,73]),
[iquote('1:SSi:13887.1,13887.0,73.1,73.1,73.1')] ).
cnf(14272,plain,
( ~ aElement0(u)
| ~ aElement0(skf36(u,smndt0(sz10)))
| ~ doDivides0(smndt0(sz10),u)
| ~ equal(u,xa)
| skP4(smndt0(sz10)) ),
inference(spl,[status(thm),theory(equality)],[1142,841]),
[iquote('0:SpL:1142.2,841.1')] ).
cnf(14279,plain,
( ~ aElement0(u)
| ~ doDivides0(smndt0(sz10),u)
| ~ equal(u,xa)
| skP4(smndt0(sz10)) ),
inference(ssi,[status(thm)],[14272,35,73,2,849,853]),
[iquote('0:SSi:14272.1,35.0,73.0,2.0,849.1,853.0')] ).
cnf(14280,plain,
( ~ doDivides0(smndt0(sz10),u)
| ~ equal(u,xa)
| skP4(smndt0(sz10)) ),
inference(mrr,[status(thm)],[14279,500]),
[iquote('0:MRR:14279.0,500.1')] ).
cnf(19746,plain,
( ~ aElement0(skc69)
| ~ aElement0(xu)
| equal(sdtasdt0(smndt0(sz10),xa),smndt0(xa)) ),
inference(spr,[status(thm),theory(equality)],[70,3196]),
[iquote('0:SpR:70.0,3196.2')] ).
cnf(19774,plain,
equal(sdtasdt0(smndt0(sz10),xa),smndt0(xa)),
inference(ssi,[status(thm)],[19746,274,815,16,12850]),
[iquote('0:SSi:19746.1,19746.0,274.0,815.0,16.0,12850.0')] ).
cnf(25794,plain,
( ~ aElement0(skc72)
| ~ aElement0(u)
| ~ aElement0(skc73)
| equal(sdtpldt0(skc73,sdtpldt0(u,skc72)),sdtpldt0(u,xb)) ),
inference(spr,[status(thm),theory(equality)],[72,3074]),
[iquote('0:SpR:72.0,3074.3')] ).
cnf(25944,plain,
( ~ aElement0(skc72)
| ~ aElement0(u)
| ~ aElement0(skc73)
| equal(sdtpldt0(skc72,sdtpldt0(skc73,u)),sdtpldt0(u,xb)) ),
inference(rew,[status(thm),theory(equality)],[3088,25794]),
[iquote('0:Rew:3088.3,25794.3')] ).
cnf(25945,plain,
( ~ aElement0(skc72)
| ~ aElement0(u)
| ~ aElement0(skc73)
| equal(sdtpldt0(xb,u),sdtpldt0(u,xb)) ),
inference(rew,[status(thm),theory(equality)],[7997,25944]),
[iquote('0:Rew:7997.1,25944.3')] ).
cnf(25946,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xb,u),sdtpldt0(u,xb)) ),
inference(ssi,[status(thm)],[25945,283,279]),
[iquote('0:SSi:25945.2,25945.0,283.0,279.0')] ).
cnf(28895,plain,
( ~ aElement0(xu)
| ~ aElement0(u)
| ~ aElement0(skc69)
| ~ equal(sdtasdt0(u,xa),xa)
| skP4(sdtasdt0(u,xu)) ),
inference(spl,[status(thm),theory(equality)],[70,8833]),
[iquote('0:SpL:70.0,8833.3')] ).
cnf(28949,plain,
( ~ aElement0(u)
| ~ equal(sdtasdt0(u,xa),xa)
| skP4(sdtasdt0(u,xu)) ),
inference(ssi,[status(thm)],[28895,16,12850,274,815]),
[iquote('0:SSi:28895.2,28895.0,16.0,12850.0,274.0,815.0')] ).
cnf(31321,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(u))
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(spr,[status(thm),theory(equality)],[13888,7722]),
[iquote('1:SpR:13888.1,7722.2')] ).
cnf(31328,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| equal(sdtasdt0(xq,xu),smndt0(sdtpldt0(skc71,skc70))) ),
inference(spr,[status(thm),theory(equality)],[93,13888]),
[iquote('1:SpR:93.0,13888.1')] ).
cnf(31365,plain,
equal(sdtasdt0(xq,xu),smndt0(sdtpldt0(skc71,skc70))),
inference(ssi,[status(thm)],[31328,109,17,274,815]),
[iquote('1:SSi:31328.0,109.0,17.0,274.0,815.2')] ).
cnf(31367,plain,
equal(smndt0(smndt0(sdtpldt0(skc71,skc70))),sdtpldt0(skc71,skc70)),
inference(rew,[status(thm),theory(equality)],[31365,93]),
[iquote('1:Rew:31365.0,93.0')] ).
cnf(31451,plain,
equal(sdtpldt0(smndt0(sdtpldt0(skc71,skc70)),skc58),sdtpldt0(xb,smndt0(xr))),
inference(rew,[status(thm),theory(equality)],[31365,12917]),
[iquote('1:Rew:31365.0,12917.0')] ).
cnf(31639,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(ssi,[status(thm)],[31321,73]),
[iquote('1:SSi:31321.1,73.1')] ).
cnf(31641,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,smndt0(sdtpldt0(v,smndt0(u)))),u) ),
inference(rew,[status(thm),theory(equality)],[31639,8526]),
[iquote('1:Rew:31639.2,8526.2')] ).
cnf(32481,plain,
( ~ aElement0(xu)
| ~ aElement0(xq)
| equal(sdtpldt0(smndt0(sdtpldt0(skc71,skc70)),skc58),smndt0(sdtpldt0(skc71,skc70))) ),
inference(spr,[status(thm),theory(equality)],[31365,8369]),
[iquote('1:SpR:31365.0,8369.2')] ).
cnf(32538,plain,
( ~ aElement0(xu)
| ~ aElement0(xq)
| equal(smndt0(sdtpldt0(skc71,skc70)),sdtpldt0(xb,smndt0(xr))) ),
inference(rew,[status(thm),theory(equality)],[31451,32481]),
[iquote('1:Rew:31451.0,32481.2')] ).
cnf(32539,plain,
equal(smndt0(sdtpldt0(skc71,skc70)),sdtpldt0(xb,smndt0(xr))),
inference(ssi,[status(thm)],[32538,17,274,815]),
[iquote('1:SSi:32538.1,32538.0,17.0,274.0,815.0')] ).
cnf(32541,plain,
equal(sdtpldt0(skc71,skc70),smndt0(sdtpldt0(xb,smndt0(xr)))),
inference(rew,[status(thm),theory(equality)],[32539,31367]),
[iquote('1:Rew:32539.0,31367.0')] ).
cnf(32750,plain,
~ equal(sdtpldt0(xb,smndt0(sdtpldt0(xb,smndt0(xr)))),xr),
inference(rew,[status(thm),theory(equality)],[32541,723]),
[iquote('1:Rew:32541.0,723.0')] ).
cnf(33654,plain,
( ~ aElement0(xr)
| ~ aElement0(xb)
| ~ equal(xr,xr) ),
inference(spl,[status(thm),theory(equality)],[31641,32750]),
[iquote('1:SpL:31641.2,32750.0')] ).
cnf(33655,plain,
( ~ aElement0(xr)
| ~ aElement0(xb) ),
inference(obv,[status(thm),theory(equality)],[33654]),
[iquote('1:Obv:33654.2')] ).
cnf(33656,plain,
$false,
inference(ssi,[status(thm)],[33655,4,18]),
[iquote('1:SSi:33655.1,33655.0,4.0,18.0')] ).
cnf(33717,plain,
~ equal(skc60,skc58),
inference(spt,[spt(split,[position(sa)])],[33656,1382]),
[iquote('1:Spt:33656.0,1283.0,1382.0')] ).
cnf(33718,plain,
equal(skc60,xa),
inference(spt,[spt(split,[position(s2)])],[1283]),
[iquote('1:Spt:33656.0,1283.1')] ).
cnf(33723,plain,
equal(smndt0(xa),xa),
inference(rew,[status(thm),theory(equality)],[33718,1221]),
[iquote('1:Rew:33718.0,1221.0')] ).
cnf(33734,plain,
equal(sdtasdt0(smndt0(sz10),xa),xa),
inference(rew,[status(thm),theory(equality)],[33723,19774]),
[iquote('1:Rew:33723.0,19774.0')] ).
cnf(33797,plain,
( ~ equal(xa,xa)
| skP3(xb) ),
inference(rew,[status(thm),theory(equality)],[33718,1243]),
[iquote('1:Rew:33718.0,1243.0')] ).
cnf(33798,plain,
skP3(xb),
inference(obv,[status(thm),theory(equality)],[33797]),
[iquote('1:Obv:33797.0')] ).
cnf(33813,plain,
( ~ equal(xa,xa)
| skP4(xb) ),
inference(rew,[status(thm),theory(equality)],[33718,1244]),
[iquote('1:Rew:33718.0,1244.0')] ).
cnf(33814,plain,
skP4(xb),
inference(obv,[status(thm),theory(equality)],[33813]),
[iquote('1:Obv:33813.0')] ).
cnf(33940,plain,
( ~ aElement0(u)
| equal(sdtasdt0(xa,u),xa) ),
inference(rew,[status(thm),theory(equality)],[33718,1216]),
[iquote('1:Rew:33718.0,1216.1')] ).
cnf(34067,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,xa),u) ),
inference(rew,[status(thm),theory(equality)],[33718,1219]),
[iquote('1:Rew:33718.0,1219.1')] ).
cnf(34074,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xa,u),u) ),
inference(rew,[status(thm),theory(equality)],[33718,1218]),
[iquote('1:Rew:33718.0,1218.1')] ).
cnf(34081,plain,
( ~ aElement0(u)
| equal(sdtasdt0(u,xa),xa) ),
inference(rew,[status(thm),theory(equality)],[33718,1217]),
[iquote('1:Rew:33718.0,1217.1')] ).
cnf(34110,plain,
( ~ aElement0(u)
| ~ equal(xa,xa)
| skP4(sdtasdt0(u,xu)) ),
inference(rew,[status(thm),theory(equality)],[34081,28949]),
[iquote('1:Rew:34081.1,28949.1')] ).
cnf(34138,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,smndt0(u)),xa) ),
inference(rew,[status(thm),theory(equality)],[33718,1229]),
[iquote('1:Rew:33718.0,1229.1')] ).
cnf(34222,plain,
( ~ aElement0(u)
| skP4(sdtasdt0(u,xu)) ),
inference(obv,[status(thm),theory(equality)],[34110]),
[iquote('1:Obv:34110.1')] ).
cnf(34462,plain,
( ~ aElement0(xa)
| doDivides0(smndt0(sz10),xa) ),
inference(spr,[status(thm),theory(equality)],[33723,7650]),
[iquote('1:SpR:33723.0,7650.1')] ).
cnf(34472,plain,
doDivides0(smndt0(sz10),xa),
inference(ssi,[status(thm)],[34462,3,819]),
[iquote('1:SSi:34462.0,3.0,819.0')] ).
cnf(34521,plain,
( ~ aElement0(xa)
| ~ aElement0(u)
| ~ aElement0(smndt0(sz10))
| ~ equal(xa,u)
| doDivides0(smndt0(sz10),u) ),
inference(res,[status(thm),theory(equality)],[34472,2827]),
[iquote('1:Res:34472.0,2827.3')] ).
cnf(34522,plain,
( ~ aElement0(u)
| ~ equal(xa,u)
| doDivides0(smndt0(sz10),u) ),
inference(ssi,[status(thm)],[34521,73,2,849,853,3,819]),
[iquote('1:SSi:34521.2,34521.0,73.0,2.0,849.0,853.0,3.0,819.1')] ).
cnf(34523,plain,
( ~ equal(xa,u)
| doDivides0(smndt0(sz10),u) ),
inference(mrr,[status(thm)],[34522,500]),
[iquote('1:MRR:34522.0,500.1')] ).
cnf(34525,plain,
( ~ equal(u,xa)
| skP4(smndt0(sz10)) ),
inference(mrr,[status(thm)],[14280,34523]),
[iquote('1:MRR:14280.0,34523.1')] ).
cnf(34526,plain,
skP4(smndt0(sz10)),
inference(aed,[status(thm),theory(equality)],[32,34525]),
[iquote('1:AED:32.0,34525.0')] ).
cnf(34835,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| ~ aElement0(xa)
| ~ equal(sdtasdt0(u,xa),xa)
| skP4(sdtasdt0(u,smndt0(sz10))) ),
inference(spl,[status(thm),theory(equality)],[33734,8833]),
[iquote('1:SpL:33734.0,8833.3')] ).
cnf(34861,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| ~ aElement0(xa)
| ~ equal(sdtasdt0(u,xa),xa)
| skP4(smndt0(u)) ),
inference(rew,[status(thm),theory(equality)],[111,34835]),
[iquote('1:Rew:111.1,34835.4')] ).
cnf(34862,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| ~ aElement0(xa)
| ~ equal(xa,xa)
| skP4(smndt0(u)) ),
inference(rew,[status(thm),theory(equality)],[34081,34861]),
[iquote('1:Rew:34081.1,34861.3')] ).
cnf(34863,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(u)
| ~ aElement0(xa)
| skP4(smndt0(u)) ),
inference(obv,[status(thm),theory(equality)],[34862]),
[iquote('1:Obv:34862.3')] ).
cnf(34864,plain,
( ~ aElement0(u)
| skP4(smndt0(u)) ),
inference(ssi,[status(thm)],[34863,3,819,34526,73,2,849,853]),
[iquote('1:SSi:34863.2,34863.0,3.0,819.0,34526.0,73.1,2.0,849.0,853.0')] ).
cnf(35074,plain,
( ~ aElement0(skf48(u))
| ~ aElementOf0(u,slsdtgt0(xa))
| equal(xa,u) ),
inference(spr,[status(thm),theory(equality)],[33940,124]),
[iquote('1:SpR:33940.1,124.1')] ).
cnf(35186,plain,
( ~ aElementOf0(u,slsdtgt0(xa))
| equal(xa,u) ),
inference(ssi,[status(thm)],[35074,27]),
[iquote('1:SSi:35074.0,27.0')] ).
cnf(36522,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| skP4(sdtpldt0(skc71,skc70)) ),
inference(spr,[status(thm),theory(equality)],[93,34864]),
[iquote('1:SpR:93.0,34864.1')] ).
cnf(36524,plain,
skP4(sdtpldt0(skc71,skc70)),
inference(ssi,[status(thm)],[36522,109,17,274,815]),
[iquote('1:SSi:36522.0,109.0,17.0,274.0,815.2')] ).
cnf(36757,plain,
( ~ aElement0(u)
| ~ aElement0(xa)
| ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,xa)),sdtasdt0(v,u)) ),
inference(spr,[status(thm),theory(equality)],[34067,170]),
[iquote('1:SpR:34067.1,170.3')] ).
cnf(36805,plain,
( ~ aElement0(xa)
| ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,xa)),sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[36757]),
[iquote('1:Obv:36757.0')] ).
cnf(36806,plain,
( ~ aElement0(xa)
| ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),xa),sdtasdt0(v,u)) ),
inference(rew,[status(thm),theory(equality)],[34081,36805]),
[iquote('1:Rew:34081.1,36805.3')] ).
cnf(36807,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),xa),sdtasdt0(v,u)) ),
inference(ssi,[status(thm)],[36806,3,819]),
[iquote('1:SSi:36806.0,3.0,819.0')] ).
cnf(37299,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(u))
| ~ aElement0(u)
| equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(xa,v)) ),
inference(spr,[status(thm),theory(equality)],[34138,166]),
[iquote('1:SpR:34138.1,166.3')] ).
cnf(37315,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(xa,u)) ),
inference(obv,[status(thm),theory(equality)],[37299]),
[iquote('1:Obv:37299.0')] ).
cnf(37316,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[34074,37315]),
[iquote('1:Rew:34074.1,37315.3')] ).
cnf(37317,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[37316,73,34864]),
[iquote('1:SSi:37316.1,73.1,34864.1')] ).
cnf(38771,plain,
equal(skc71,xa),
inference(res,[status(thm),theory(equality)],[51,35186]),
[iquote('1:Res:51.0,35186.0')] ).
cnf(38774,plain,
equal(skf46(u),xa),
inference(res,[status(thm),theory(equality)],[60,35186]),
[iquote('1:Res:60.0,35186.0')] ).
cnf(39119,plain,
equal(smndt0(sdtasdt0(xq,xu)),sdtpldt0(xa,skc70)),
inference(rew,[status(thm),theory(equality)],[38771,93]),
[iquote('1:Rew:38771.0,93.0')] ).
cnf(39121,plain,
~ equal(sdtpldt0(sdtpldt0(xa,skc70),xb),xr),
inference(rew,[status(thm),theory(equality)],[38771,190]),
[iquote('1:Rew:38771.0,190.0')] ).
cnf(39122,plain,
skP4(sdtpldt0(xa,skc70)),
inference(rew,[status(thm),theory(equality)],[38771,36524]),
[iquote('1:Rew:38771.0,36524.0')] ).
cnf(39523,plain,
( ~ aElementOf0(u,xI)
| equal(sdtpldt0(xa,skf45(u)),u) ),
inference(rew,[status(thm),theory(equality)],[38774,122]),
[iquote('1:Rew:38774.0,122.1')] ).
cnf(40987,plain,
( ~ aElement0(skc70)
| ~ equal(sdtpldt0(skc70,xb),xr) ),
inference(spl,[status(thm),theory(equality)],[34074,39121]),
[iquote('1:SpL:34074.1,39121.0')] ).
cnf(40991,plain,
( ~ aElement0(skc70)
| ~ equal(sdtpldt0(xb,skc70),xr) ),
inference(rew,[status(thm),theory(equality)],[25946,40987]),
[iquote('1:Rew:25946.1,40987.1')] ).
cnf(40992,plain,
~ equal(sdtpldt0(xb,skc70),xr),
inference(ssi,[status(thm)],[40991,280]),
[iquote('1:SSi:40991.0,280.0')] ).
cnf(41003,plain,
( ~ aElement0(skf45(u))
| ~ aElementOf0(u,xI)
| equal(skf45(u),u) ),
inference(spr,[status(thm),theory(equality)],[39523,34074]),
[iquote('1:SpR:39523.1,34074.1')] ).
cnf(41014,plain,
( ~ aElementOf0(u,xI)
| equal(skf45(u),u) ),
inference(ssi,[status(thm)],[41003,289]),
[iquote('1:SSi:41003.0,289.0')] ).
cnf(41015,plain,
( ~ aElementOf0(u,xI)
| equal(sdtpldt0(xa,u),u) ),
inference(rew,[status(thm),theory(equality)],[41014,39523]),
[iquote('1:Rew:41014.1,39523.1')] ).
cnf(41179,plain,
( ~ aElementOf0(skc70,xI)
| skP4(skc70) ),
inference(spr,[status(thm),theory(equality)],[41015,39122]),
[iquote('1:SpR:41015.1,39122.0')] ).
cnf(41190,plain,
skP4(skc70),
inference(mrr,[status(thm)],[41179,5182]),
[iquote('1:MRR:41179.0,5182.0')] ).
cnf(43323,plain,
( ~ aElement0(xr)
| ~ aElement0(smndt0(xr))
| equal(sdtpldt0(sdtasdt0(xq,xu),xa),sdtpldt0(xb,smndt0(xr))) ),
inference(spr,[status(thm),theory(equality)],[34138,3054]),
[iquote('1:SpR:34138.1,3054.1')] ).
cnf(43336,plain,
equal(sdtpldt0(sdtasdt0(xq,xu),xa),sdtpldt0(xb,smndt0(xr))),
inference(ssi,[status(thm)],[43323,73,18,34864]),
[iquote('1:SSi:43323.1,43323.0,73.0,18.0,34864.1,18.0,18.1')] ).
cnf(44127,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(smndt0(smndt0(u)))
| ~ aElement0(u)
| equal(sdtpldt0(u,xa),smndt0(smndt0(u))) ),
inference(spr,[status(thm),theory(equality)],[34138,37317]),
[iquote('1:SpR:34138.1,37317.2')] ).
cnf(44143,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(smndt0(smndt0(u)))
| ~ aElement0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(rew,[status(thm),theory(equality)],[34067,44127]),
[iquote('1:Rew:34067.1,44127.3')] ).
cnf(44144,plain,
( ~ aElement0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(ssi,[status(thm)],[44143,73,34864]),
[iquote('1:SSi:44143.1,44143.0,73.1,73.1,34864.1,34864.1,73.1,34864.1,73.1,34864.1')] ).
cnf(44959,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(u))
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(spr,[status(thm),theory(equality)],[44144,7722]),
[iquote('1:SpR:44144.1,7722.2')] ).
cnf(44979,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| equal(sdtasdt0(xq,xu),smndt0(sdtpldt0(xa,skc70))) ),
inference(spr,[status(thm),theory(equality)],[39119,44144]),
[iquote('1:SpR:39119.0,44144.1')] ).
cnf(45008,plain,
equal(sdtasdt0(xq,xu),smndt0(sdtpldt0(xa,skc70))),
inference(ssi,[status(thm)],[44979,34222,17,109,274,815]),
[iquote('1:SSi:44979.0,34222.0,17.0,109.0,17.2,274.0,815.1')] ).
cnf(45009,plain,
equal(sdtpldt0(smndt0(sdtpldt0(xa,skc70)),xr),xb),
inference(rew,[status(thm),theory(equality)],[45008,83]),
[iquote('1:Rew:45008.0,83.0')] ).
cnf(45010,plain,
equal(sdtpldt0(xr,smndt0(sdtpldt0(xa,skc70))),xb),
inference(rew,[status(thm),theory(equality)],[45008,717]),
[iquote('1:Rew:45008.0,717.0')] ).
cnf(45011,plain,
equal(smndt0(smndt0(sdtpldt0(xa,skc70))),sdtpldt0(xa,skc70)),
inference(rew,[status(thm),theory(equality)],[45008,39119]),
[iquote('1:Rew:45008.0,39119.0')] ).
cnf(45163,plain,
equal(sdtpldt0(smndt0(sdtpldt0(xa,skc70)),xa),sdtpldt0(xb,smndt0(xr))),
inference(rew,[status(thm),theory(equality)],[45008,43336]),
[iquote('1:Rew:45008.0,43336.0')] ).
cnf(45246,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(ssi,[status(thm)],[44959,73,34864]),
[iquote('1:SSi:44959.1,73.1,34864.1')] ).
cnf(45247,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,smndt0(sdtpldt0(v,smndt0(u)))),u) ),
inference(rew,[status(thm),theory(equality)],[45246,37317]),
[iquote('1:Rew:45246.2,37317.2')] ).
cnf(45338,plain,
( ~ aElement0(skc70)
| equal(sdtpldt0(smndt0(skc70),xr),xb) ),
inference(spr,[status(thm),theory(equality)],[34074,45009]),
[iquote('1:SpR:34074.1,45009.0')] ).
cnf(45342,plain,
equal(sdtpldt0(smndt0(skc70),xr),xb),
inference(ssi,[status(thm)],[45338,280,41190]),
[iquote('1:SSi:45338.0,280.0,41190.0')] ).
cnf(45350,plain,
( ~ aElement0(xr)
| ~ aElement0(smndt0(skc70))
| equal(sdtpldt0(xr,smndt0(skc70)),xb) ),
inference(spr,[status(thm),theory(equality)],[45342,128]),
[iquote('1:SpR:45342.0,128.2')] ).
cnf(45369,plain,
equal(sdtpldt0(xr,smndt0(skc70)),xb),
inference(ssi,[status(thm)],[45350,73,280,41190,34864,18]),
[iquote('1:SSi:45350.1,45350.0,73.0,280.0,41190.0,34864.1,280.0,41190.0,18.1')] ).
cnf(45435,plain,
( ~ aElementOf0(skc70,xI)
| equal(smndt0(smndt0(skc70)),skc70) ),
inference(spr,[status(thm),theory(equality)],[41015,45011]),
[iquote('1:SpR:41015.1,45011.0')] ).
cnf(45444,plain,
equal(smndt0(smndt0(skc70)),skc70),
inference(mrr,[status(thm)],[45435,5182]),
[iquote('1:MRR:45435.0,5182.0')] ).
cnf(46017,plain,
( ~ aElement0(xu)
| ~ aElement0(xq)
| equal(sdtpldt0(smndt0(sdtpldt0(xa,skc70)),xa),smndt0(sdtpldt0(xa,skc70))) ),
inference(spr,[status(thm),theory(equality)],[45008,36807]),
[iquote('1:SpR:45008.0,36807.2')] ).
cnf(46067,plain,
( ~ aElement0(xu)
| ~ aElement0(xq)
| equal(sdtpldt0(xb,smndt0(xr)),smndt0(sdtpldt0(xa,skc70))) ),
inference(rew,[status(thm),theory(equality)],[45163,46017]),
[iquote('1:Rew:45163.0,46017.2')] ).
cnf(46068,plain,
equal(sdtpldt0(xb,smndt0(xr)),smndt0(sdtpldt0(xa,skc70))),
inference(ssi,[status(thm)],[46067,17,274,815]),
[iquote('1:SSi:46067.1,46067.0,17.0,274.0,815.0')] ).
cnf(46248,plain,
( ~ aElement0(skc70)
| ~ aElement0(xr)
| equal(sdtpldt0(xr,smndt0(xb)),skc70) ),
inference(spr,[status(thm),theory(equality)],[45369,45247]),
[iquote('1:SpR:45369.0,45247.2')] ).
cnf(46250,plain,
( ~ aElement0(sdtpldt0(xa,skc70))
| ~ aElement0(xr)
| equal(sdtpldt0(xr,smndt0(xb)),sdtpldt0(xa,skc70)) ),
inference(spr,[status(thm),theory(equality)],[45010,45247]),
[iquote('1:SpR:45010.0,45247.2')] ).
cnf(46257,plain,
equal(sdtpldt0(xr,smndt0(xb)),skc70),
inference(ssi,[status(thm)],[46248,18,280,41190]),
[iquote('1:SSi:46248.1,46248.0,18.0,280.0,41190.0')] ).
cnf(46269,plain,
( ~ aElement0(sdtpldt0(xa,skc70))
| ~ aElement0(xr)
| equal(sdtpldt0(xa,skc70),skc70) ),
inference(rew,[status(thm),theory(equality)],[46257,46250]),
[iquote('1:Rew:46257.0,46250.2')] ).
cnf(46270,plain,
equal(sdtpldt0(xa,skc70),skc70),
inference(ssi,[status(thm)],[46269,18,39122,108,3,819,280,41190]),
[iquote('1:SSi:46269.1,46269.0,18.0,39122.0,108.0,3.0,819.2,280.0,41190.0')] ).
cnf(46431,plain,
equal(sdtpldt0(xb,smndt0(xr)),smndt0(skc70)),
inference(rew,[status(thm),theory(equality)],[46270,46068]),
[iquote('1:Rew:46270.0,46068.0')] ).
cnf(46945,plain,
( ~ aElement0(xr)
| ~ aElement0(xb)
| equal(sdtpldt0(xb,smndt0(smndt0(skc70))),xr) ),
inference(spr,[status(thm),theory(equality)],[46431,45247]),
[iquote('1:SpR:46431.0,45247.2')] ).
cnf(46951,plain,
( ~ aElement0(xr)
| ~ aElement0(xb)
| equal(sdtpldt0(xb,skc70),xr) ),
inference(rew,[status(thm),theory(equality)],[45444,46945]),
[iquote('1:Rew:45444.0,46945.2')] ).
cnf(46952,plain,
equal(sdtpldt0(xb,skc70),xr),
inference(ssi,[status(thm)],[46951,4,33798,33814,18]),
[iquote('1:SSi:46951.1,46951.0,4.0,33798.0,33814.0,18.0')] ).
cnf(46953,plain,
$false,
inference(mrr,[status(thm)],[46952,40992]),
[iquote('1:MRR:46952.0,40992.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG122+4 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 14:50:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 31.60/31.82
% 31.60/31.82 SPASS V 3.9
% 31.60/31.82 SPASS beiseite: Proof found.
% 31.60/31.82 % SZS status Theorem
% 31.60/31.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.60/31.82 SPASS derived 32274 clauses, backtracked 1823 clauses, performed 16 splits and kept 13449 clauses.
% 31.60/31.82 SPASS allocated 135411 KBytes.
% 31.60/31.82 SPASS spent 0:0:31.42 on the problem.
% 31.60/31.82 0:00:00.04 for the input.
% 31.60/31.82 0:00:00.30 for the FLOTTER CNF translation.
% 31.60/31.82 0:00:00.40 for inferences.
% 31.60/31.82 0:00:01.14 for the backtracking.
% 31.60/31.82 0:0:29.23 for the reduction.
% 31.60/31.82
% 31.60/31.82
% 31.60/31.82 Here is a proof with depth 5, length 332 :
% 31.60/31.82 % SZS output start Refutation
% See solution above
% 38.21/38.41 Formulae used in the proof : mSortsC mSortsC_01 m__2091 m__2174 m__2666 m__2699 m__2203 m__2479 m__2228 m__2273 mUnNeZr mDefDiv m__2690 mDefIdeal mSortsU mPrIdeal mAddZero mMulUnit mMulZero m__ mAddInvr mEOfElem m__2612 mSortsB mSortsB_02 mMulMnOne mAddComm mMulComm m__2129 mCancel mMulAsso mAddAsso mAMDistr
% 38.21/38.41
%------------------------------------------------------------------------------