%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG069+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 20:41:23 EDT 2022
% Result : Theorem 146.53s 146.76s
% Output : Refutation 166.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 29
% Syntax : Number of clauses : 103 ( 28 unt; 0 nHn; 103 RR)
% Number of literals : 281 ( 0 equ; 188 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
aScalar0(xA),
file('RNG069+1.p',unknown),
[] ).
cnf(8,axiom,
aScalar0(xB),
file('RNG069+1.p',unknown),
[] ).
cnf(9,axiom,
aScalar0(xC),
file('RNG069+1.p',unknown),
[] ).
cnf(10,axiom,
aScalar0(xD),
file('RNG069+1.p',unknown),
[] ).
cnf(11,axiom,
aScalar0(xE),
file('RNG069+1.p',unknown),
[] ).
cnf(12,axiom,
aScalar0(xF),
file('RNG069+1.p',unknown),
[] ).
cnf(13,axiom,
aScalar0(xG),
file('RNG069+1.p',unknown),
[] ).
cnf(14,axiom,
aScalar0(xH),
file('RNG069+1.p',unknown),
[] ).
cnf(15,axiom,
aScalar0(xR),
file('RNG069+1.p',unknown),
[] ).
cnf(16,axiom,
aScalar0(xP),
file('RNG069+1.p',unknown),
[] ).
cnf(17,axiom,
aScalar0(xS),
file('RNG069+1.p',unknown),
[] ).
cnf(28,axiom,
equal(sdtasdt0(xA,xA),xF),
file('RNG069+1.p',unknown),
[] ).
cnf(29,axiom,
equal(sdtasdt0(xB,xB),xG),
file('RNG069+1.p',unknown),
[] ).
cnf(30,axiom,
equal(sdtasdt0(xA,xB),xH),
file('RNG069+1.p',unknown),
[] ).
cnf(31,axiom,
equal(sdtasdt0(xC,xG),xR),
file('RNG069+1.p',unknown),
[] ).
cnf(32,axiom,
equal(sdtasdt0(xE,xH),xP),
file('RNG069+1.p',unknown),
[] ).
cnf(33,axiom,
equal(sdtasdt0(xF,xD),xS),
file('RNG069+1.p',unknown),
[] ).
cnf(34,axiom,
equal(sdtasdt0(xR,xS),xN),
file('RNG069+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ aScalar0(u)
| aScalar0(smndt0(u)) ),
file('RNG069+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aScalar0(u)
| equal(smndt0(smndt0(u)),u) ),
file('RNG069+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| aScalar0(sdtasdt0(v,u)) ),
file('RNG069+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('RNG069+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(v,smndt0(u)),smndt0(sdtasdt0(v,u))) ),
file('RNG069+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(smndt0(v),u),smndt0(sdtasdt0(v,u))) ),
file('RNG069+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(smndt0(v),smndt0(u)),sdtasdt0(v,u)) ),
file('RNG069+1.p',unknown),
[] ).
cnf(68,axiom,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('RNG069+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('RNG069+1.p',unknown),
[] ).
cnf(86,axiom,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
file('RNG069+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| ~ aScalar0(x)
| equal(sdtasdt0(sdtpldt0(x,w),sdtpldt0(v,u)),sdtpldt0(sdtpldt0(sdtasdt0(x,v),sdtasdt0(x,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u)))) ),
file('RNG069+1.p',unknown),
[] ).
cnf(93,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(rew,[status(thm),theory(equality)],[34,86]),
[iquote('0:Rew:34.0,86.0')] ).
cnf(188,plain,
( ~ aScalar0(xD)
| ~ aScalar0(xF)
| equal(sdtasdt0(xD,xF),xS) ),
inference(spr,[status(thm),theory(equality)],[61,33]),
[iquote('0:SpR:61.2,33.0')] ).
cnf(210,plain,
equal(sdtasdt0(xD,xF),xS),
inference(ssi,[status(thm)],[188,12,10]),
[iquote('0:SSi:188.1,188.0,12.0,10.0')] ).
cnf(307,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(smndt0(u))
| equal(smndt0(sdtasdt0(smndt0(u),v)),sdtasdt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[50,65]),
[iquote('0:SpR:50.1,65.2')] ).
cnf(314,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(smndt0(u))
| equal(smndt0(smndt0(sdtasdt0(u,v))),sdtasdt0(u,v)) ),
inference(rew,[status(thm),theory(equality)],[65,307]),
[iquote('0:Rew:65.2,307.3')] ).
cnf(315,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(smndt0(smndt0(sdtasdt0(u,v))),sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[314,37]),
[iquote('0:SSi:314.2,37.1')] ).
cnf(451,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| ~ aScalar0(smndt0(sdtasdt0(u,v)))
| equal(sdtasdt0(smndt0(sdtasdt0(u,v)),w),sdtasdt0(sdtasdt0(u,v),smndt0(w))) ),
inference(spr,[status(thm),theory(equality)],[315,66]),
[iquote('0:SpR:315.2,66.2')] ).
cnf(455,plain,
( ~ aScalar0(xE)
| ~ aScalar0(xH)
| equal(smndt0(smndt0(xP)),xP) ),
inference(spr,[status(thm),theory(equality)],[32,315]),
[iquote('0:SpR:32.0,315.2')] ).
cnf(470,plain,
equal(smndt0(smndt0(xP)),xP),
inference(ssi,[status(thm)],[455,14,11]),
[iquote('0:SSi:455.1,455.0,14.0,11.0')] ).
cnf(495,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(smndt0(sdtasdt0(u,v)),w),sdtasdt0(sdtasdt0(u,v),smndt0(w))) ),
inference(ssi,[status(thm)],[451,37,56]),
[iquote('0:SSi:451.3,37.2,56.1')] ).
cnf(551,plain,
( ~ aScalar0(u)
| ~ aScalar0(smndt0(xP))
| equal(sdtasdt0(smndt0(xP),u),sdtasdt0(xP,smndt0(u))) ),
inference(spr,[status(thm),theory(equality)],[470,66]),
[iquote('0:SpR:470.0,66.2')] ).
cnf(552,plain,
( ~ aScalar0(u)
| ~ aScalar0(smndt0(xP))
| equal(smndt0(sdtasdt0(smndt0(xP),u)),sdtasdt0(xP,u)) ),
inference(spr,[status(thm),theory(equality)],[470,65]),
[iquote('0:SpR:470.0,65.2')] ).
cnf(558,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(smndt0(xP),u),sdtasdt0(xP,smndt0(u))) ),
inference(ssi,[status(thm)],[551,37,16]),
[iquote('0:SSi:551.1,37.0,16.1')] ).
cnf(559,plain,
( ~ aScalar0(u)
| ~ aScalar0(smndt0(xP))
| equal(smndt0(sdtasdt0(xP,smndt0(u))),sdtasdt0(xP,u)) ),
inference(rew,[status(thm),theory(equality)],[558,552]),
[iquote('0:Rew:558.1,552.2')] ).
cnf(560,plain,
( ~ aScalar0(u)
| equal(smndt0(sdtasdt0(xP,smndt0(u))),sdtasdt0(xP,u)) ),
inference(ssi,[status(thm)],[559,37,16]),
[iquote('0:SSi:559.1,37.0,16.1')] ).
cnf(903,plain,
( ~ aScalar0(smndt0(u))
| ~ aScalar0(v)
| ~ aScalar0(w)
| ~ aScalar0(u)
| ~ aScalar0(sdtasdt0(w,v))
| equal(smndt0(sdtasdt0(sdtasdt0(w,v),u)),sdtasdt0(w,sdtasdt0(v,smndt0(u)))) ),
inference(spr,[status(thm),theory(equality)],[75,64]),
[iquote('0:SpR:75.3,64.2')] ).
cnf(906,plain,
( ~ aScalar0(u)
| ~ aScalar0(xD)
| ~ aScalar0(xF)
| equal(sdtasdt0(xS,u),sdtasdt0(xF,sdtasdt0(xD,u))) ),
inference(spr,[status(thm),theory(equality)],[33,75]),
[iquote('0:SpR:33.0,75.3')] ).
cnf(907,plain,
( ~ aScalar0(u)
| ~ aScalar0(xH)
| ~ aScalar0(xE)
| equal(sdtasdt0(xP,u),sdtasdt0(xE,sdtasdt0(xH,u))) ),
inference(spr,[status(thm),theory(equality)],[32,75]),
[iquote('0:SpR:32.0,75.3')] ).
cnf(908,plain,
( ~ aScalar0(u)
| ~ aScalar0(xG)
| ~ aScalar0(xC)
| equal(sdtasdt0(xR,u),sdtasdt0(xC,sdtasdt0(xG,u))) ),
inference(spr,[status(thm),theory(equality)],[31,75]),
[iquote('0:SpR:31.0,75.3')] ).
cnf(909,plain,
( ~ aScalar0(u)
| ~ aScalar0(xB)
| ~ aScalar0(xA)
| equal(sdtasdt0(xH,u),sdtasdt0(xA,sdtasdt0(xB,u))) ),
inference(spr,[status(thm),theory(equality)],[30,75]),
[iquote('0:SpR:30.0,75.3')] ).
cnf(910,plain,
( ~ aScalar0(u)
| ~ aScalar0(xB)
| ~ aScalar0(xB)
| equal(sdtasdt0(xG,u),sdtasdt0(xB,sdtasdt0(xB,u))) ),
inference(spr,[status(thm),theory(equality)],[29,75]),
[iquote('0:SpR:29.0,75.3')] ).
cnf(911,plain,
( ~ aScalar0(u)
| ~ aScalar0(xA)
| ~ aScalar0(xA)
| equal(sdtasdt0(xF,u),sdtasdt0(xA,sdtasdt0(xA,u))) ),
inference(spr,[status(thm),theory(equality)],[28,75]),
[iquote('0:SpR:28.0,75.3')] ).
cnf(916,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| ~ aScalar0(v)
| ~ aScalar0(u)
| equal(sdtasdt0(sdtasdt0(v,u),w),sdtasdt0(u,sdtasdt0(v,w))) ),
inference(spr,[status(thm),theory(equality)],[61,75]),
[iquote('0:SpR:61.2,75.3')] ).
cnf(917,plain,
( ~ aScalar0(u)
| ~ aScalar0(xF)
| ~ aScalar0(xD)
| equal(sdtasdt0(xS,u),sdtasdt0(xD,sdtasdt0(xF,u))) ),
inference(spr,[status(thm),theory(equality)],[210,75]),
[iquote('0:SpR:210.0,75.3')] ).
cnf(919,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| ~ aScalar0(smndt0(u))
| ~ aScalar0(v)
| equal(sdtasdt0(smndt0(sdtasdt0(v,u)),w),sdtasdt0(v,sdtasdt0(smndt0(u),w))) ),
inference(spr,[status(thm),theory(equality)],[64,75]),
[iquote('0:SpR:64.2,75.3')] ).
cnf(922,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xS,u),sdtasdt0(xF,sdtasdt0(xD,u))) ),
inference(ssi,[status(thm)],[906,12,10]),
[iquote('0:SSi:906.2,906.1,12.0,10.0')] ).
cnf(926,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xP,u),sdtasdt0(xE,sdtasdt0(xH,u))) ),
inference(ssi,[status(thm)],[907,11,14]),
[iquote('0:SSi:907.2,907.1,11.0,14.0')] ).
cnf(927,plain,
( ~ aScalar0(u)
| equal(smndt0(sdtasdt0(xP,smndt0(u))),sdtasdt0(xE,sdtasdt0(xH,u))) ),
inference(rew,[status(thm),theory(equality)],[926,560]),
[iquote('0:Rew:926.1,560.1')] ).
cnf(928,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xR,u),sdtasdt0(xC,sdtasdt0(xG,u))) ),
inference(ssi,[status(thm)],[908,9,13]),
[iquote('0:SSi:908.2,908.1,9.0,13.0')] ).
cnf(930,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xH,u),sdtasdt0(xA,sdtasdt0(xB,u))) ),
inference(ssi,[status(thm)],[909,7,8]),
[iquote('0:SSi:909.2,909.1,7.0,8.0')] ).
cnf(932,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xP,u),sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u)))) ),
inference(rew,[status(thm),theory(equality)],[930,926]),
[iquote('0:Rew:930.1,926.1')] ).
cnf(933,plain,
( ~ aScalar0(u)
| equal(smndt0(sdtasdt0(xP,smndt0(u))),sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u)))) ),
inference(rew,[status(thm),theory(equality)],[930,927]),
[iquote('0:Rew:930.1,927.1')] ).
cnf(934,plain,
( ~ aScalar0(u)
| ~ aScalar0(xB)
| equal(sdtasdt0(xG,u),sdtasdt0(xB,sdtasdt0(xB,u))) ),
inference(obv,[status(thm),theory(equality)],[910]),
[iquote('0:Obv:910.1')] ).
cnf(935,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xG,u),sdtasdt0(xB,sdtasdt0(xB,u))) ),
inference(ssi,[status(thm)],[934,8]),
[iquote('0:SSi:934.1,8.0')] ).
cnf(937,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xR,u),sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,u)))) ),
inference(rew,[status(thm),theory(equality)],[935,928]),
[iquote('0:Rew:935.1,928.1')] ).
cnf(939,plain,
( ~ aScalar0(u)
| ~ aScalar0(xA)
| equal(sdtasdt0(xF,u),sdtasdt0(xA,sdtasdt0(xA,u))) ),
inference(obv,[status(thm),theory(equality)],[911]),
[iquote('0:Obv:911.1')] ).
cnf(940,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xF,u),sdtasdt0(xA,sdtasdt0(xA,u))) ),
inference(ssi,[status(thm)],[939,7]),
[iquote('0:SSi:939.1,7.0')] ).
cnf(942,plain,
( ~ aScalar0(u)
| ~ aScalar0(xF)
| ~ aScalar0(xD)
| equal(sdtasdt0(xF,sdtasdt0(xD,u)),sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,u)))) ),
inference(rew,[status(thm),theory(equality)],[922,917,940]),
[iquote('0:Rew:922.1,917.3,940.1,917.3')] ).
cnf(943,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xF,sdtasdt0(xD,u)),sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,u)))) ),
inference(ssi,[status(thm)],[942,10,12]),
[iquote('0:SSi:942.2,942.1,10.0,12.0')] ).
cnf(944,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xS,u),sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,u)))) ),
inference(rew,[status(thm),theory(equality)],[943,922]),
[iquote('0:Rew:943.1,922.1')] ).
cnf(960,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(sdtasdt0(v,w),u),sdtasdt0(w,sdtasdt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[916]),
[iquote('0:Obv:916.1')] ).
cnf(961,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(v,sdtasdt0(w,u)),sdtasdt0(w,sdtasdt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[75,960]),
[iquote('0:Rew:75.3,960.3')] ).
cnf(971,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(smndt0(u))
| ~ aScalar0(w)
| equal(sdtasdt0(smndt0(sdtasdt0(w,u)),v),sdtasdt0(w,sdtasdt0(smndt0(u),v))) ),
inference(obv,[status(thm),theory(equality)],[919]),
[iquote('0:Obv:919.1')] ).
cnf(972,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(smndt0(u))
| ~ aScalar0(w)
| equal(sdtasdt0(smndt0(sdtasdt0(w,u)),v),sdtasdt0(w,smndt0(sdtasdt0(u,v)))) ),
inference(rew,[status(thm),theory(equality)],[65,971]),
[iquote('0:Rew:65.2,971.4')] ).
cnf(973,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(smndt0(u))
| ~ aScalar0(w)
| equal(sdtasdt0(sdtasdt0(w,u),smndt0(v)),sdtasdt0(w,smndt0(sdtasdt0(u,v)))) ),
inference(rew,[status(thm),theory(equality)],[495,972]),
[iquote('0:Rew:495.3,972.4')] ).
cnf(974,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(sdtasdt0(w,u),smndt0(v)),sdtasdt0(w,smndt0(sdtasdt0(u,v)))) ),
inference(ssi,[status(thm)],[973,37]),
[iquote('0:SSi:973.2,37.1')] ).
cnf(983,plain,
( ~ aScalar0(smndt0(u))
| ~ aScalar0(v)
| ~ aScalar0(w)
| ~ aScalar0(u)
| ~ aScalar0(sdtasdt0(w,v))
| equal(sdtasdt0(w,smndt0(sdtasdt0(v,u))),smndt0(sdtasdt0(w,sdtasdt0(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[75,903,64]),
[iquote('0:Rew:75.3,903.5,64.2,903.5')] ).
cnf(984,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(v,smndt0(sdtasdt0(u,w))),smndt0(sdtasdt0(v,sdtasdt0(u,w)))) ),
inference(ssi,[status(thm)],[983,56,37]),
[iquote('0:SSi:983.4,983.0,56.1,37.2')] ).
cnf(988,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(sdtasdt0(w,u),smndt0(v)),smndt0(sdtasdt0(w,sdtasdt0(u,v)))) ),
inference(rew,[status(thm),theory(equality)],[984,974]),
[iquote('0:Rew:984.3,974.3')] ).
cnf(1913,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xR)
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(sdtasdt0(xR,xS),sdtasdt0(xS,xS)))) ),
inference(spr,[status(thm),theory(equality)],[61,93]),
[iquote('0:SpR:61.2,93.0')] ).
cnf(1946,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xR)
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(xN,sdtasdt0(xS,xS)))) ),
inference(rew,[status(thm),theory(equality)],[34,1913]),
[iquote('0:Rew:34.0,1913.2')] ).
cnf(1947,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xR)
| sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))) ),
inference(rew,[status(thm),theory(equality)],[937,1946,944]),
[iquote('0:Rew:937.1,1946.2,944.1,1946.2')] ).
cnf(1948,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))),
inference(ssi,[status(thm)],[1947,15,17]),
[iquote('0:SSi:1947.1,1947.0,15.0,17.0')] ).
cnf(2590,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xR)
| ~ aScalar0(xS)
| ~ aScalar0(xR)
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))) ),
inference(spl,[status(thm),theory(equality)],[91,68]),
[iquote('0:SpL:91.4,68.0')] ).
cnf(2598,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xR)
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))) ),
inference(obv,[status(thm),theory(equality)],[2590]),
[iquote('0:Obv:2590.1')] ).
cnf(2599,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xR)
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(xN,sdtasdt0(xS,xS)))) ),
inference(rew,[status(thm),theory(equality)],[34,2598,61]),
[iquote('0:Rew:34.0,2598.2,61.2,2598.2')] ).
cnf(2600,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xR)
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))) ),
inference(rew,[status(thm),theory(equality)],[937,2599,944]),
[iquote('0:Rew:937.1,2599.2,944.1,2599.2')] ).
cnf(2601,plain,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))),
inference(ssi,[status(thm)],[2600,15,17]),
[iquote('0:SSi:2600.1,2600.0,15.0,17.0')] ).
cnf(10519,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(xH)
| ~ aScalar0(sdtasdt0(v,u))
| equal(sdtasdt0(v,sdtasdt0(xH,u)),sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(v,u)))) ),
inference(spr,[status(thm),theory(equality)],[961,930]),
[iquote('0:SpR:961.3,930.1')] ).
cnf(10986,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(xH)
| ~ aScalar0(sdtasdt0(v,u))
| equal(sdtasdt0(v,sdtasdt0(xA,sdtasdt0(xB,u))),sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(v,u)))) ),
inference(rew,[status(thm),theory(equality)],[930,10519]),
[iquote('0:Rew:930.1,10519.4')] ).
cnf(10987,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(v,sdtasdt0(xA,sdtasdt0(xB,u))),sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(v,u)))) ),
inference(ssi,[status(thm)],[10986,56,14]),
[iquote('0:SSi:10986.3,10986.2,56.0,14.2')] ).
cnf(13460,plain,
( ~ aScalar0(xH)
| ~ aScalar0(u)
| ~ aScalar0(xE)
| equal(sdtasdt0(xP,smndt0(u)),smndt0(sdtasdt0(xE,sdtasdt0(xH,u)))) ),
inference(spr,[status(thm),theory(equality)],[32,988]),
[iquote('0:SpR:32.0,988.3')] ).
cnf(13561,plain,
( ~ aScalar0(xH)
| ~ aScalar0(u)
| ~ aScalar0(xE)
| equal(sdtasdt0(xP,smndt0(u)),smndt0(sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u))))) ),
inference(rew,[status(thm),theory(equality)],[930,13460]),
[iquote('0:Rew:930.1,13460.3')] ).
cnf(13562,plain,
( ~ aScalar0(xH)
| ~ aScalar0(u)
| ~ aScalar0(xE)
| equal(sdtasdt0(xP,smndt0(u)),smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,u))))) ),
inference(rew,[status(thm),theory(equality)],[10987,13561]),
[iquote('0:Rew:10987.2,13561.3')] ).
cnf(13563,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xP,smndt0(u)),smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,u))))) ),
inference(ssi,[status(thm)],[13562,11,14]),
[iquote('0:SSi:13562.2,13562.0,11.0,14.0')] ).
cnf(13567,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,u)))))) ),
inference(rew,[status(thm),theory(equality)],[13563,933]),
[iquote('0:Rew:13563.1,933.1')] ).
cnf(13708,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xP,u),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,u)))))) ),
inference(rew,[status(thm),theory(equality)],[13567,932]),
[iquote('0:Rew:13567.1,932.1')] ).
cnf(33669,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| ~ aScalar0(xP)
| ~ aScalar0(xP)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))) ),
inference(spl,[status(thm),theory(equality)],[91,2601]),
[iquote('0:SpL:91.4,2601.0')] ).
cnf(33701,plain,
( ~ aScalar0(xP)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))) ),
inference(obv,[status(thm),theory(equality)],[33669]),
[iquote('0:Obv:33669.2')] ).
cnf(33702,plain,
( ~ aScalar0(xP)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP)))))),sdtpldt0(smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))))),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))) ),
inference(rew,[status(thm),theory(equality)],[13708,33701]),
[iquote('0:Rew:13708.1,33701.1')] ).
cnf(33703,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP)))))),sdtpldt0(smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))))),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))),
inference(ssi,[status(thm)],[33702,16]),
[iquote('0:SSi:33702.0,16.0')] ).
cnf(53314,plain,
( ~ aScalar0(xP)
| sdtlseqdt0(sdtpldt0(sdtpldt0(smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP)))))),sdtpldt0(smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))))),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))) ),
inference(spr,[status(thm),theory(equality)],[13708,1948]),
[iquote('0:SpR:13708.1,1948.0')] ).
cnf(53387,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP)))))),sdtpldt0(smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,xP))))))),sdtpldt0(sdtpldt0(sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,xR))),xN),sdtpldt0(xN,sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,xS)))))),
inference(ssi,[status(thm)],[53314,16]),
[iquote('0:SSi:53314.0,16.0')] ).
cnf(53388,plain,
$false,
inference(mrr,[status(thm)],[53387,33703]),
[iquote('0:MRR:53387.0,33703.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG069+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 08:24:19 EDT 2022
% 0.14/0.34 % CPUTime :
% 146.53/146.76
% 146.53/146.76 SPASS V 3.9
% 146.53/146.76 SPASS beiseite: Proof found.
% 146.53/146.76 % SZS status Theorem
% 146.53/146.76 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 146.53/146.76 SPASS derived 25773 clauses, backtracked 0 clauses, performed 0 splits and kept 9686 clauses.
% 146.53/146.76 SPASS allocated 167919 KBytes.
% 146.53/146.76 SPASS spent 0:2:26.37 on the problem.
% 146.53/146.76 0:00:00.04 for the input.
% 146.53/146.76 0:00:00.04 for the FLOTTER CNF translation.
% 146.53/146.76 0:00:00.46 for inferences.
% 146.53/146.76 0:00:00.00 for the backtracking.
% 146.53/146.76 0:2:25.59 for the reduction.
% 146.53/146.76
% 146.53/146.76
% 146.53/146.76 Here is a proof with depth 3, length 103 :
% 146.53/146.76 % SZS output start Refutation
% See solution above
% 166.95/167.11 Formulae used in the proof : m__1746 m__1766 m__1783 m__1800 m__1820 m__1837 m__1854 m__1873 m__1892 m__1911 m__1930 m__1949 mNegSc mScZero mMulSc mArith mMNeg mMDNeg m__ m__2580 mDistr2
% 166.95/167.11
%------------------------------------------------------------------------------