TSTP Solution File: RNG069+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG069+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 187.80s 188.13s
% Output : Refutation 210.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 29
% Syntax : Number of clauses : 99 ( 28 unt; 0 nHn; 99 RR)
% Number of literals : 266 ( 0 equ; 177 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+2.p',unknown),
[] ).
cnf(8,axiom,
aScalar0(xB),
file('RNG069+2.p',unknown),
[] ).
cnf(9,axiom,
aScalar0(xC),
file('RNG069+2.p',unknown),
[] ).
cnf(10,axiom,
aScalar0(xD),
file('RNG069+2.p',unknown),
[] ).
cnf(11,axiom,
aScalar0(xE),
file('RNG069+2.p',unknown),
[] ).
cnf(12,axiom,
aScalar0(xF),
file('RNG069+2.p',unknown),
[] ).
cnf(13,axiom,
aScalar0(xG),
file('RNG069+2.p',unknown),
[] ).
cnf(14,axiom,
aScalar0(xH),
file('RNG069+2.p',unknown),
[] ).
cnf(15,axiom,
aScalar0(xR),
file('RNG069+2.p',unknown),
[] ).
cnf(16,axiom,
aScalar0(xP),
file('RNG069+2.p',unknown),
[] ).
cnf(17,axiom,
aScalar0(xS),
file('RNG069+2.p',unknown),
[] ).
cnf(28,axiom,
equal(sdtasdt0(xA,xA),xF),
file('RNG069+2.p',unknown),
[] ).
cnf(29,axiom,
equal(sdtasdt0(xB,xB),xG),
file('RNG069+2.p',unknown),
[] ).
cnf(30,axiom,
equal(sdtasdt0(xA,xB),xH),
file('RNG069+2.p',unknown),
[] ).
cnf(31,axiom,
equal(sdtasdt0(xC,xG),xR),
file('RNG069+2.p',unknown),
[] ).
cnf(32,axiom,
equal(sdtasdt0(xE,xH),xP),
file('RNG069+2.p',unknown),
[] ).
cnf(33,axiom,
equal(sdtasdt0(xF,xD),xS),
file('RNG069+2.p',unknown),
[] ).
cnf(34,axiom,
equal(sdtasdt0(xR,xS),xN),
file('RNG069+2.p',unknown),
[] ).
cnf(37,axiom,
( ~ aScalar0(u)
| aScalar0(smndt0(u)) ),
file('RNG069+2.p',unknown),
[] ).
cnf(52,axiom,
( ~ aScalar0(u)
| equal(smndt0(smndt0(u)),u) ),
file('RNG069+2.p',unknown),
[] ).
cnf(58,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| aScalar0(sdtasdt0(v,u)) ),
file('RNG069+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('RNG069+2.p',unknown),
[] ).
cnf(68,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(v,smndt0(u)),smndt0(sdtasdt0(v,u))) ),
file('RNG069+2.p',unknown),
[] ).
cnf(69,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(smndt0(v),u),smndt0(sdtasdt0(v,u))) ),
file('RNG069+2.p',unknown),
[] ).
cnf(70,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(smndt0(v),smndt0(u)),sdtasdt0(v,u)) ),
file('RNG069+2.p',unknown),
[] ).
cnf(72,axiom,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('RNG069+2.p',unknown),
[] ).
cnf(79,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('RNG069+2.p',unknown),
[] ).
cnf(90,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+2.p',unknown),
[] ).
cnf(95,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+2.p',unknown),
[] ).
cnf(98,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)],[34,90]),
[iquote('0:Rew:34.0,90.0')] ).
cnf(213,plain,
( ~ aScalar0(xD)
| ~ aScalar0(xF)
| equal(sdtasdt0(xD,xF),xS) ),
inference(spr,[status(thm),theory(equality)],[65,33]),
[iquote('0:SpR:65.2,33.0')] ).
cnf(235,plain,
equal(sdtasdt0(xD,xF),xS),
inference(ssi,[status(thm)],[213,12,10]),
[iquote('0:SSi:213.1,213.0,12.0,10.0')] ).
cnf(332,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(smndt0(u))
| equal(smndt0(sdtasdt0(smndt0(u),v)),sdtasdt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[52,69]),
[iquote('0:SpR:52.1,69.2')] ).
cnf(339,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(smndt0(u))
| equal(smndt0(smndt0(sdtasdt0(u,v))),sdtasdt0(u,v)) ),
inference(rew,[status(thm),theory(equality)],[69,332]),
[iquote('0:Rew:69.2,332.3')] ).
cnf(340,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(smndt0(smndt0(sdtasdt0(u,v))),sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[339,37]),
[iquote('0:SSi:339.2,37.1')] ).
cnf(783,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)],[79,68]),
[iquote('0:SpR:79.3,68.2')] ).
cnf(787,plain,
( ~ aScalar0(u)
| ~ aScalar0(xD)
| ~ aScalar0(xF)
| equal(sdtasdt0(xS,u),sdtasdt0(xF,sdtasdt0(xD,u))) ),
inference(spr,[status(thm),theory(equality)],[33,79]),
[iquote('0:SpR:33.0,79.3')] ).
cnf(788,plain,
( ~ aScalar0(u)
| ~ aScalar0(xH)
| ~ aScalar0(xE)
| equal(sdtasdt0(xP,u),sdtasdt0(xE,sdtasdt0(xH,u))) ),
inference(spr,[status(thm),theory(equality)],[32,79]),
[iquote('0:SpR:32.0,79.3')] ).
cnf(789,plain,
( ~ aScalar0(u)
| ~ aScalar0(xG)
| ~ aScalar0(xC)
| equal(sdtasdt0(xR,u),sdtasdt0(xC,sdtasdt0(xG,u))) ),
inference(spr,[status(thm),theory(equality)],[31,79]),
[iquote('0:SpR:31.0,79.3')] ).
cnf(790,plain,
( ~ aScalar0(u)
| ~ aScalar0(xB)
| ~ aScalar0(xA)
| equal(sdtasdt0(xH,u),sdtasdt0(xA,sdtasdt0(xB,u))) ),
inference(spr,[status(thm),theory(equality)],[30,79]),
[iquote('0:SpR:30.0,79.3')] ).
cnf(791,plain,
( ~ aScalar0(u)
| ~ aScalar0(xB)
| ~ aScalar0(xB)
| equal(sdtasdt0(xG,u),sdtasdt0(xB,sdtasdt0(xB,u))) ),
inference(spr,[status(thm),theory(equality)],[29,79]),
[iquote('0:SpR:29.0,79.3')] ).
cnf(792,plain,
( ~ aScalar0(u)
| ~ aScalar0(xA)
| ~ aScalar0(xA)
| equal(sdtasdt0(xF,u),sdtasdt0(xA,sdtasdt0(xA,u))) ),
inference(spr,[status(thm),theory(equality)],[28,79]),
[iquote('0:SpR:28.0,79.3')] ).
cnf(797,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)],[65,79]),
[iquote('0:SpR:65.2,79.3')] ).
cnf(798,plain,
( ~ aScalar0(u)
| ~ aScalar0(xF)
| ~ aScalar0(xD)
| equal(sdtasdt0(xS,u),sdtasdt0(xD,sdtasdt0(xF,u))) ),
inference(spr,[status(thm),theory(equality)],[235,79]),
[iquote('0:SpR:235.0,79.3')] ).
cnf(800,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)],[68,79]),
[iquote('0:SpR:68.2,79.3')] ).
cnf(802,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xS,u),sdtasdt0(xF,sdtasdt0(xD,u))) ),
inference(ssi,[status(thm)],[787,12,10]),
[iquote('0:SSi:787.2,787.1,12.0,10.0')] ).
cnf(804,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xP,u),sdtasdt0(xE,sdtasdt0(xH,u))) ),
inference(ssi,[status(thm)],[788,11,14]),
[iquote('0:SSi:788.2,788.1,11.0,14.0')] ).
cnf(805,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xR,u),sdtasdt0(xC,sdtasdt0(xG,u))) ),
inference(ssi,[status(thm)],[789,9,13]),
[iquote('0:SSi:789.2,789.1,9.0,13.0')] ).
cnf(806,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xH,u),sdtasdt0(xA,sdtasdt0(xB,u))) ),
inference(ssi,[status(thm)],[790,7,8]),
[iquote('0:SSi:790.2,790.1,7.0,8.0')] ).
cnf(807,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xP,u),sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u)))) ),
inference(rew,[status(thm),theory(equality)],[806,804]),
[iquote('0:Rew:806.1,804.1')] ).
cnf(808,plain,
( ~ aScalar0(u)
| ~ aScalar0(xB)
| equal(sdtasdt0(xG,u),sdtasdt0(xB,sdtasdt0(xB,u))) ),
inference(obv,[status(thm),theory(equality)],[791]),
[iquote('0:Obv:791.1')] ).
cnf(809,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xG,u),sdtasdt0(xB,sdtasdt0(xB,u))) ),
inference(ssi,[status(thm)],[808,8]),
[iquote('0:SSi:808.1,8.0')] ).
cnf(810,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xR,u),sdtasdt0(xC,sdtasdt0(xB,sdtasdt0(xB,u)))) ),
inference(rew,[status(thm),theory(equality)],[809,805]),
[iquote('0:Rew:809.1,805.1')] ).
cnf(811,plain,
( ~ aScalar0(u)
| ~ aScalar0(xA)
| equal(sdtasdt0(xF,u),sdtasdt0(xA,sdtasdt0(xA,u))) ),
inference(obv,[status(thm),theory(equality)],[792]),
[iquote('0:Obv:792.1')] ).
cnf(812,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xF,u),sdtasdt0(xA,sdtasdt0(xA,u))) ),
inference(ssi,[status(thm)],[811,7]),
[iquote('0:SSi:811.1,7.0')] ).
cnf(813,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)],[802,798,812]),
[iquote('0:Rew:802.1,798.3,812.1,798.3')] ).
cnf(814,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xF,sdtasdt0(xD,u)),sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,u)))) ),
inference(ssi,[status(thm)],[813,10,12]),
[iquote('0:SSi:813.2,813.1,10.0,12.0')] ).
cnf(815,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xS,u),sdtasdt0(xD,sdtasdt0(xA,sdtasdt0(xA,u)))) ),
inference(rew,[status(thm),theory(equality)],[814,802]),
[iquote('0:Rew:814.1,802.1')] ).
cnf(829,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(sdtasdt0(v,w),u),sdtasdt0(w,sdtasdt0(v,u))) ),
inference(obv,[status(thm),theory(equality)],[797]),
[iquote('0:Obv:797.1')] ).
cnf(830,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(v,sdtasdt0(w,u)),sdtasdt0(w,sdtasdt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[79,829]),
[iquote('0:Rew:79.3,829.3')] ).
cnf(840,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)],[800]),
[iquote('0:Obv:800.1')] ).
cnf(841,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)],[69,840]),
[iquote('0:Rew:69.2,840.4')] ).
cnf(842,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(smndt0(sdtasdt0(w,u)),v),sdtasdt0(w,smndt0(sdtasdt0(u,v)))) ),
inference(ssi,[status(thm)],[841,37]),
[iquote('0:SSi:841.2,37.1')] ).
cnf(848,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)],[79,783,68]),
[iquote('0:Rew:79.3,783.5,68.2,783.5')] ).
cnf(849,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(v,smndt0(sdtasdt0(u,w))),smndt0(sdtasdt0(v,sdtasdt0(u,w)))) ),
inference(ssi,[status(thm)],[848,58,37]),
[iquote('0:SSi:848.4,848.0,58.1,37.2')] ).
cnf(851,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ aScalar0(w)
| equal(sdtasdt0(smndt0(sdtasdt0(w,u)),v),smndt0(sdtasdt0(w,sdtasdt0(u,v)))) ),
inference(rew,[status(thm),theory(equality)],[849,842]),
[iquote('0:Rew:849.3,842.3')] ).
cnf(1866,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)],[65,98]),
[iquote('0:SpR:65.2,98.0')] ).
cnf(1899,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)],[34,1866]),
[iquote('0:Rew:34.0,1866.2')] ).
cnf(1900,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)],[810,1899,815]),
[iquote('0:Rew:810.1,1899.2,815.1,1899.2')] ).
cnf(1901,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)],[1900,15,17]),
[iquote('0:SSi:1900.1,1900.0,15.0,17.0')] ).
cnf(2514,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)],[95,72]),
[iquote('0:SpL:95.4,72.0')] ).
cnf(2522,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)],[2514]),
[iquote('0:Obv:2514.1')] ).
cnf(2523,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)],[34,2522,65]),
[iquote('0:Rew:34.0,2522.2,65.2,2522.2')] ).
cnf(2524,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)],[810,2523,815]),
[iquote('0:Rew:810.1,2523.2,815.1,2523.2')] ).
cnf(2525,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)],[2524,15,17]),
[iquote('0:SSi:2524.1,2524.0,15.0,17.0')] ).
cnf(3927,plain,
( ~ aScalar0(xE)
| ~ aScalar0(xH)
| equal(smndt0(smndt0(xP)),xP) ),
inference(spr,[status(thm),theory(equality)],[32,340]),
[iquote('0:SpR:32.0,340.2')] ).
cnf(3976,plain,
equal(smndt0(smndt0(xP)),xP),
inference(ssi,[status(thm)],[3927,14,11]),
[iquote('0:SSi:3927.1,3927.0,14.0,11.0')] ).
cnf(4098,plain,
( ~ aScalar0(u)
| ~ aScalar0(smndt0(xP))
| equal(sdtasdt0(smndt0(xP),u),sdtasdt0(xP,smndt0(u))) ),
inference(spr,[status(thm),theory(equality)],[3976,70]),
[iquote('0:SpR:3976.0,70.2')] ).
cnf(4099,plain,
( ~ aScalar0(u)
| ~ aScalar0(smndt0(xP))
| equal(smndt0(sdtasdt0(smndt0(xP),u)),sdtasdt0(xP,u)) ),
inference(spr,[status(thm),theory(equality)],[3976,69]),
[iquote('0:SpR:3976.0,69.2')] ).
cnf(4111,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(smndt0(xP),u),sdtasdt0(xP,smndt0(u))) ),
inference(ssi,[status(thm)],[4098,37,16]),
[iquote('0:SSi:4098.1,37.0,16.1')] ).
cnf(4112,plain,
( ~ aScalar0(u)
| ~ aScalar0(smndt0(xP))
| equal(smndt0(sdtasdt0(smndt0(xP),u)),sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u)))) ),
inference(rew,[status(thm),theory(equality)],[807,4099]),
[iquote('0:Rew:807.1,4099.2')] ).
cnf(4113,plain,
( ~ aScalar0(u)
| ~ aScalar0(smndt0(xP))
| equal(smndt0(sdtasdt0(xP,smndt0(u))),sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u)))) ),
inference(rew,[status(thm),theory(equality)],[4111,4112]),
[iquote('0:Rew:4111.1,4112.2')] ).
cnf(4114,plain,
( ~ aScalar0(u)
| equal(smndt0(sdtasdt0(xP,smndt0(u))),sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u)))) ),
inference(ssi,[status(thm)],[4113,37,16]),
[iquote('0:SSi:4113.1,37.0,16.1')] ).
cnf(15262,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)],[830,806]),
[iquote('0:SpR:830.3,806.1')] ).
cnf(15767,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)],[806,15262]),
[iquote('0:Rew:806.1,15262.4')] ).
cnf(15768,plain,
( ~ aScalar0(u)
| ~ aScalar0(v)
| equal(sdtasdt0(v,sdtasdt0(xA,sdtasdt0(xB,u))),sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(v,u)))) ),
inference(ssi,[status(thm)],[15767,58,14]),
[iquote('0:SSi:15767.3,15767.2,58.0,14.2')] ).
cnf(18984,plain,
( ~ aScalar0(xH)
| ~ aScalar0(u)
| ~ aScalar0(xE)
| equal(sdtasdt0(smndt0(xP),u),smndt0(sdtasdt0(xE,sdtasdt0(xH,u)))) ),
inference(spr,[status(thm),theory(equality)],[32,851]),
[iquote('0:SpR:32.0,851.3')] ).
cnf(19028,plain,
( ~ aScalar0(xH)
| ~ aScalar0(u)
| ~ aScalar0(xE)
| equal(sdtasdt0(smndt0(xP),u),smndt0(sdtasdt0(xE,sdtasdt0(xA,sdtasdt0(xB,u))))) ),
inference(rew,[status(thm),theory(equality)],[806,18984]),
[iquote('0:Rew:806.1,18984.3')] ).
cnf(19029,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)],[4111,19028,15768]),
[iquote('0:Rew:4111.1,19028.3,15768.2,19028.3')] ).
cnf(19030,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xP,smndt0(u)),smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,u))))) ),
inference(ssi,[status(thm)],[19029,11,14]),
[iquote('0:SSi:19029.2,19029.0,11.0,14.0')] ).
cnf(19032,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)],[19030,4114]),
[iquote('0:Rew:19030.1,4114.1')] ).
cnf(19194,plain,
( ~ aScalar0(u)
| equal(sdtasdt0(xP,u),smndt0(smndt0(sdtasdt0(xA,sdtasdt0(xB,sdtasdt0(xE,u)))))) ),
inference(rew,[status(thm),theory(equality)],[19032,807]),
[iquote('0:Rew:19032.1,807.1')] ).
cnf(42039,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)],[95,2525]),
[iquote('0:SpL:95.4,2525.0')] ).
cnf(42071,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)],[42039]),
[iquote('0:Obv:42039.2')] ).
cnf(42072,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)],[19194,42071]),
[iquote('0:Rew:19194.1,42071.1')] ).
cnf(42073,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)],[42072,16]),
[iquote('0:SSi:42072.0,16.0')] ).
cnf(60265,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)],[19194,1901]),
[iquote('0:SpR:19194.1,1901.0')] ).
cnf(60361,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)],[60265,16]),
[iquote('0:SSi:60265.0,16.0')] ).
cnf(60362,plain,
$false,
inference(mrr,[status(thm)],[60361,42073]),
[iquote('0:MRR:60361.0,42073.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG069+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon May 30 19:24:22 EDT 2022
% 0.14/0.36 % CPUTime :
% 187.80/188.13
% 187.80/188.13 SPASS V 3.9
% 187.80/188.13 SPASS beiseite: Proof found.
% 187.80/188.13 % SZS status Theorem
% 187.80/188.13 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 187.80/188.13 SPASS derived 30043 clauses, backtracked 716 clauses, performed 1 splits and kept 10946 clauses.
% 187.80/188.13 SPASS allocated 173658 KBytes.
% 187.80/188.13 SPASS spent 0:03:07.71 on the problem.
% 187.80/188.13 0:00:00.04 for the input.
% 187.80/188.13 0:00:00.04 for the FLOTTER CNF translation.
% 187.80/188.13 0:00:00.62 for inferences.
% 187.80/188.13 0:00:00.14 for the backtracking.
% 187.80/188.13 0:03:06.51 for the reduction.
% 187.80/188.13
% 187.80/188.13
% 187.80/188.13 Here is a proof with depth 3, length 99 :
% 187.80/188.13 % SZS output start Refutation
% See solution above
% 210.82/211.18 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
% 210.82/211.18
%------------------------------------------------------------------------------