TSTP Solution File: RNG082+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG082+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 20:41:25 EDT 2022
% Result : Theorem 0.47s 0.65s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of clauses : 88 ( 8 unt; 0 nHn; 88 RR)
% Number of literals : 284 ( 0 equ; 201 neg)
% Maximal clause size : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aElement0(sz00),
file('RNG082+1.p',unknown),
[] ).
cnf(2,axiom,
aElement0(sz10),
file('RNG082+1.p',unknown),
[] ).
cnf(3,axiom,
aElement0(xx),
file('RNG082+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ aElement0(u)
| aElement0(smndt0(u)) ),
file('RNG082+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(sdtasdt0(smndt0(sz10),xx),smndt0(xx)),
file('RNG082+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('RNG082+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('RNG082+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('RNG082+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('RNG082+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('RNG082+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtpldt0(v,u)) ),
file('RNG082+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtasdt0(v,u)) ),
file('RNG082+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('RNG082+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('RNG082+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('RNG082+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
file('RNG082+1.p',unknown),
[] ).
cnf(59,plain,
( ~ aElement0(xx)
| ~ aElement0(smndt0(sz10))
| ~ equal(sdtasdt0(xx,smndt0(sz10)),smndt0(xx)) ),
inference(spl,[status(thm),theory(equality)],[15,5]),
[iquote('0:SpL:15.2,5.0')] ).
cnf(65,plain,
~ equal(sdtasdt0(xx,smndt0(sz10)),smndt0(xx)),
inference(ssi,[status(thm)],[59,4,2,3]),
[iquote('0:SSi:59.1,59.0,4.0,2.0,3.1')] ).
cnf(95,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(u)
| ~ aElement0(sz00)
| equal(sdtpldt0(sz00,sdtpldt0(u,v)),sdtpldt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[7,17]),
[iquote('0:SpR:7.1,17.3')] ).
cnf(96,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(u)
| ~ aElement0(smndt0(u))
| equal(sdtpldt0(smndt0(u),sdtpldt0(u,v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[11,17]),
[iquote('0:SpR:11.1,17.3')] ).
cnf(99,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(u))
| ~ aElement0(u)
| equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[10,17]),
[iquote('0:SpR:10.1,17.3')] ).
cnf(103,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sz00)
| equal(sdtpldt0(sz00,sdtpldt0(v,u)),sdtpldt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[95]),
[iquote('0:Obv:95.0')] ).
cnf(104,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sz00,sdtpldt0(v,u)),sdtpldt0(v,u)) ),
inference(ssi,[status(thm)],[103,1]),
[iquote('0:SSi:103.2,1.0')] ).
cnf(105,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[99]),
[iquote('0:Obv:99.0')] ).
cnf(106,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[7,105]),
[iquote('0:Rew:7.1,105.3')] ).
cnf(107,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[106,4]),
[iquote('0:SSi:106.1,4.1')] ).
cnf(108,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[96]),
[iquote('0:Obv:96.0')] ).
cnf(109,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[7,108]),
[iquote('0:Rew:7.1,108.3')] ).
cnf(110,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[109,4]),
[iquote('0:SSi:109.2,4.1')] ).
cnf(134,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(smndt0(smndt0(u)))
| ~ aElement0(u)
| equal(sdtpldt0(u,sz00),smndt0(smndt0(u))) ),
inference(spr,[status(thm),theory(equality)],[10,107]),
[iquote('0:SpR:10.1,107.2')] ).
cnf(135,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(v)
| ~ aElement0(v)
| ~ aElement0(u)
| equal(sdtpldt0(u,sdtpldt0(v,smndt0(u))),v) ),
inference(spr,[status(thm),theory(equality)],[14,107]),
[iquote('0:SpR:14.2,107.2')] ).
cnf(139,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(smndt0(smndt0(u)))
| ~ aElement0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(rew,[status(thm),theory(equality)],[6,134]),
[iquote('0:Rew:6.1,134.3')] ).
cnf(140,plain,
( ~ aElement0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(ssi,[status(thm)],[139,4]),
[iquote('0:SSi:139.1,139.0,4.1,4.1,4.1')] ).
cnf(141,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(v)
| ~ aElement0(u)
| equal(sdtpldt0(u,sdtpldt0(v,smndt0(u))),v) ),
inference(obv,[status(thm),theory(equality)],[135]),
[iquote('0:Obv:135.1')] ).
cnf(142,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(u,smndt0(v))),u) ),
inference(ssi,[status(thm)],[141,4]),
[iquote('0:SSi:141.0,4.1')] ).
cnf(192,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(v)
| ~ aElement0(u)
| equal(sdtpldt0(smndt0(u),sdtpldt0(v,u)),v) ),
inference(spr,[status(thm),theory(equality)],[14,110]),
[iquote('0:SpR:14.2,110.2')] ).
cnf(203,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(u,v)),u) ),
inference(obv,[status(thm),theory(equality)],[192]),
[iquote('0:Obv:192.1')] ).
cnf(213,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sdtpldt0(u,smndt0(v)))
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),u),sdtpldt0(u,smndt0(v))) ),
inference(spr,[status(thm),theory(equality)],[142,110]),
[iquote('0:SpR:142.2,110.2')] ).
cnf(234,plain,
( ~ aElement0(u)
| ~ aElement0(sdtpldt0(u,smndt0(v)))
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),u),sdtpldt0(u,smndt0(v))) ),
inference(obv,[status(thm),theory(equality)],[213]),
[iquote('0:Obv:213.1')] ).
cnf(235,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),u),sdtpldt0(u,smndt0(v))) ),
inference(ssi,[status(thm)],[234,12,4]),
[iquote('0:SSi:234.1,12.1,4.2')] ).
cnf(244,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| ~ aElement0(sdtpldt0(u,v))
| equal(sdtpldt0(smndt0(sdtpldt0(u,v)),u),smndt0(v)) ),
inference(spr,[status(thm),theory(equality)],[203]),
[iquote('0:SpR:203.2,203.2')] ).
cnf(257,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| ~ aElement0(sdtpldt0(v,u))
| equal(sdtpldt0(smndt0(sdtpldt0(v,u)),u),smndt0(v)) ),
inference(spr,[status(thm),theory(equality)],[110,203]),
[iquote('0:SpR:110.2,203.2')] ).
cnf(258,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(v)
| ~ aElement0(sdtpldt0(u,smndt0(v)))
| equal(sdtpldt0(smndt0(sdtpldt0(u,smndt0(v))),u),v) ),
inference(spr,[status(thm),theory(equality)],[142,203]),
[iquote('0:SpR:142.2,203.2')] ).
cnf(272,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sdtpldt0(u,smndt0(v)))
| equal(sdtpldt0(smndt0(sdtpldt0(u,smndt0(v))),u),v) ),
inference(obv,[status(thm),theory(equality)],[258]),
[iquote('0:Obv:258.1')] ).
cnf(273,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sdtpldt0(u,smndt0(v)))
| equal(sdtpldt0(u,smndt0(sdtpldt0(u,smndt0(v)))),v) ),
inference(rew,[status(thm),theory(equality)],[235,272]),
[iquote('0:Rew:235.2,272.3')] ).
cnf(274,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(u,smndt0(sdtpldt0(u,smndt0(v)))),v) ),
inference(ssi,[status(thm)],[273,12,4]),
[iquote('0:SSi:273.2,12.1,4.2')] ).
cnf(275,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| ~ aElement0(sdtpldt0(v,u))
| equal(sdtpldt0(u,smndt0(sdtpldt0(v,u))),smndt0(v)) ),
inference(rew,[status(thm),theory(equality)],[235,257]),
[iquote('0:Rew:235.2,257.4')] ).
cnf(276,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(u,smndt0(sdtpldt0(v,u))),smndt0(v)) ),
inference(ssi,[status(thm)],[275,12,4]),
[iquote('0:SSi:275.3,275.2,12.1,4.2')] ).
cnf(282,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| ~ aElement0(sdtpldt0(u,v))
| equal(sdtpldt0(u,smndt0(sdtpldt0(u,v))),smndt0(v)) ),
inference(rew,[status(thm),theory(equality)],[235,244]),
[iquote('0:Rew:235.2,244.4')] ).
cnf(283,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(u,smndt0(sdtpldt0(u,v))),smndt0(v)) ),
inference(ssi,[status(thm)],[282,12,4]),
[iquote('0:SSi:282.3,282.2,12.1,4.2')] ).
cnf(350,plain,
( ~ aElement0(u)
| ~ aElement0(u)
| ~ aElement0(smndt0(u))
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(spr,[status(thm),theory(equality)],[11,104]),
[iquote('0:SpR:11.1,104.2')] ).
cnf(362,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(u))
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(obv,[status(thm),theory(equality)],[350]),
[iquote('0:Obv:350.0')] ).
cnf(363,plain,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(ssi,[status(thm)],[362,4]),
[iquote('0:SSi:362.1,4.1')] ).
cnf(379,plain,
equal(sdtpldt0(sz00,sz00),sz00),
inference(ems,[status(thm)],[363,1]),
[iquote('0:EmS:363.0,1.0')] ).
cnf(454,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(u))
| ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,smndt0(u))),sdtasdt0(v,sz00)) ),
inference(spr,[status(thm),theory(equality)],[10,19]),
[iquote('0:SpR:10.1,19.3')] ).
cnf(461,plain,
( ~ aElement0(sz00)
| ~ aElement0(sz00)
| ~ aElement0(u)
| equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(spr,[status(thm),theory(equality)],[379,19]),
[iquote('0:SpR:379.0,19.3')] ).
cnf(462,plain,
( ~ aElement0(sz00)
| ~ aElement0(u)
| equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(obv,[status(thm),theory(equality)],[461]),
[iquote('0:Obv:461.0')] ).
cnf(463,plain,
( ~ aElement0(u)
| equal(sdtpldt0(sdtasdt0(u,sz00),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(ssi,[status(thm)],[462,1]),
[iquote('0:SSi:462.0,1.0')] ).
cnf(468,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,smndt0(u))),sdtasdt0(v,sz00)) ),
inference(obv,[status(thm),theory(equality)],[454]),
[iquote('0:Obv:454.0')] ).
cnf(469,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,smndt0(u))),sdtasdt0(v,sz00)) ),
inference(ssi,[status(thm)],[468,4]),
[iquote('0:SSi:468.0,4.1')] ).
cnf(508,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(u,sz00))
| ~ aElement0(sdtasdt0(u,sz00))
| equal(sdtpldt0(smndt0(sdtasdt0(u,sz00)),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(spr,[status(thm),theory(equality)],[463,203]),
[iquote('0:SpR:463.1,203.2')] ).
cnf(530,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(u,sz00))
| equal(sdtpldt0(smndt0(sdtasdt0(u,sz00)),sdtasdt0(u,sz00)),sdtasdt0(u,sz00)) ),
inference(obv,[status(thm),theory(equality)],[508]),
[iquote('0:Obv:508.1')] ).
cnf(531,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(u,sz00))
| equal(sdtasdt0(u,sz00),sz00) ),
inference(rew,[status(thm),theory(equality)],[11,530]),
[iquote('0:Rew:11.1,530.2')] ).
cnf(532,plain,
( ~ aElement0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
inference(ssi,[status(thm)],[531,13,1]),
[iquote('0:SSi:531.1,13.0,1.2')] ).
cnf(536,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtasdt0(v,u),sdtasdt0(v,smndt0(u))),sz00) ),
inference(rew,[status(thm),theory(equality)],[532,469]),
[iquote('0:Rew:532.1,469.2')] ).
cnf(747,plain,
( ~ aElement0(sz00)
| ~ aElement0(u)
| ~ aElement0(smndt0(sdtpldt0(sz00,smndt0(u))))
| equal(smndt0(sdtpldt0(sz00,smndt0(u))),u) ),
inference(spr,[status(thm),theory(equality)],[274,7]),
[iquote('0:SpR:274.2,7.1')] ).
cnf(748,plain,
( ~ aElement0(smndt0(u))
| ~ aElement0(v)
| ~ aElement0(smndt0(sdtpldt0(smndt0(u),smndt0(v))))
| ~ aElement0(u)
| equal(smndt0(sdtpldt0(smndt0(u),smndt0(v))),sdtpldt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[274,107]),
[iquote('0:SpR:274.2,107.2')] ).
cnf(776,plain,
( ~ aElement0(u)
| equal(smndt0(sdtpldt0(sz00,smndt0(u))),u) ),
inference(ssi,[status(thm)],[747,4,12,1]),
[iquote('0:SSi:747.2,747.0,4.0,12.1,1.0,4.2,1.1')] ).
cnf(795,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(smndt0(sdtpldt0(smndt0(v),smndt0(u))),sdtpldt0(v,u)) ),
inference(ssi,[status(thm)],[748,4,12]),
[iquote('0:SSi:748.2,748.0,4.1,12.1,4.1,4.2,4.1')] ).
cnf(804,plain,
( ~ aElement0(u)
| ~ aElement0(sdtpldt0(sz00,smndt0(u)))
| equal(sdtpldt0(sz00,smndt0(u)),smndt0(u)) ),
inference(spr,[status(thm),theory(equality)],[776,140]),
[iquote('0:SpR:776.1,140.1')] ).
cnf(821,plain,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,smndt0(u)),smndt0(u)) ),
inference(ssi,[status(thm)],[804,12,1,4]),
[iquote('0:SSi:804.1,12.1,1.0,4.2')] ).
cnf(908,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(u)
| ~ aElement0(smndt0(sdtpldt0(v,u)))
| equal(sdtpldt0(smndt0(smndt0(sdtpldt0(v,u))),smndt0(v)),u) ),
inference(spr,[status(thm),theory(equality)],[276,203]),
[iquote('0:SpR:276.2,203.2')] ).
cnf(958,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(sdtpldt0(u,v)))
| equal(sdtpldt0(smndt0(smndt0(sdtpldt0(u,v))),smndt0(u)),v) ),
inference(obv,[status(thm),theory(equality)],[908]),
[iquote('0:Obv:908.0')] ).
cnf(959,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(smndt0(sdtpldt0(u,v))),smndt0(u)),v) ),
inference(ssi,[status(thm)],[958,4,12]),
[iquote('0:SSi:958.2,4.2,12.1')] ).
cnf(1075,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| ~ aElement0(sdtpldt0(v,u))
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(spr,[status(thm),theory(equality)],[110,283]),
[iquote('0:SpR:110.2,283.2')] ).
cnf(1108,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(ssi,[status(thm)],[1075,12,4]),
[iquote('0:SSi:1075.3,1075.2,12.1,4.2')] ).
cnf(1109,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(smndt0(smndt0(sdtpldt0(v,u))),sdtpldt0(v,u)) ),
inference(rew,[status(thm),theory(equality)],[1108,795]),
[iquote('0:Rew:1108.2,795.2')] ).
cnf(1111,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sdtpldt0(u,v),smndt0(u)),v) ),
inference(rew,[status(thm),theory(equality)],[1109,959]),
[iquote('0:Rew:1109.2,959.2')] ).
cnf(1375,plain,
( ~ aElement0(u)
| ~ aElement0(sz10)
| ~ aElement0(u)
| equal(sdtpldt0(u,sdtasdt0(u,smndt0(sz10))),sz00) ),
inference(spr,[status(thm),theory(equality)],[8,536]),
[iquote('0:SpR:8.1,536.2')] ).
cnf(1388,plain,
( ~ aElement0(sz10)
| ~ aElement0(u)
| equal(sdtpldt0(u,sdtasdt0(u,smndt0(sz10))),sz00) ),
inference(obv,[status(thm),theory(equality)],[1375]),
[iquote('0:Obv:1375.0')] ).
cnf(1389,plain,
( ~ aElement0(u)
| equal(sdtpldt0(u,sdtasdt0(u,smndt0(sz10))),sz00) ),
inference(ssi,[status(thm)],[1388,2]),
[iquote('0:SSi:1388.0,2.0')] ).
cnf(1772,plain,
( ~ aElement0(u)
| ~ aElement0(u)
| ~ aElement0(sdtasdt0(u,smndt0(sz10)))
| equal(sdtasdt0(u,smndt0(sz10)),sdtpldt0(sz00,smndt0(u))) ),
inference(spr,[status(thm),theory(equality)],[1389,1111]),
[iquote('0:SpR:1389.1,1111.2')] ).
cnf(1796,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(u,smndt0(sz10)))
| equal(sdtasdt0(u,smndt0(sz10)),sdtpldt0(sz00,smndt0(u))) ),
inference(obv,[status(thm),theory(equality)],[1772]),
[iquote('0:Obv:1772.0')] ).
cnf(1797,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(u,smndt0(sz10)))
| equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
inference(rew,[status(thm),theory(equality)],[821,1796]),
[iquote('0:Rew:821.1,1796.2')] ).
cnf(1798,plain,
( ~ aElement0(u)
| equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
inference(ssi,[status(thm)],[1797,13,4,2]),
[iquote('0:SSi:1797.1,13.0,4.1,2.2')] ).
cnf(1938,plain,
( ~ aElement0(xx)
| ~ equal(smndt0(xx),smndt0(xx)) ),
inference(spl,[status(thm),theory(equality)],[1798,65]),
[iquote('0:SpL:1798.1,65.0')] ).
cnf(1939,plain,
~ aElement0(xx),
inference(obv,[status(thm),theory(equality)],[1938]),
[iquote('0:Obv:1938.1')] ).
cnf(1940,plain,
$false,
inference(ssi,[status(thm)],[1939,3]),
[iquote('0:SSi:1939.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG082+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 05:32:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.47/0.65
% 0.47/0.65 SPASS V 3.9
% 0.47/0.65 SPASS beiseite: Proof found.
% 0.47/0.65 % SZS status Theorem
% 0.47/0.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.65 SPASS derived 1001 clauses, backtracked 0 clauses, performed 0 splits and kept 203 clauses.
% 0.47/0.65 SPASS allocated 105915 KBytes.
% 0.47/0.65 SPASS spent 0:00:00.30 on the problem.
% 0.47/0.65 0:00:00.04 for the input.
% 0.47/0.65 0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.65 0:00:00.01 for inferences.
% 0.47/0.65 0:00:00.00 for the backtracking.
% 0.47/0.65 0:00:00.20 for the reduction.
% 0.47/0.65
% 0.47/0.65
% 0.47/0.65 Here is a proof with depth 6, length 88 :
% 0.47/0.65 % SZS output start Refutation
% See solution above
% 0.47/0.70 Formulae used in the proof : mSortsC mSortsC_01 m__444 mSortsU m__ mAddZero mMulUnit mAddInvr mSortsB mSortsB_02 mAddComm mMulComm mAddAsso mAMDistr
% 0.47/0.70
%------------------------------------------------------------------------------