TSTP Solution File: RNG097+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG097+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 20:41:27 EDT 2022
% Result : Theorem 0.69s 0.89s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of clauses : 49 ( 17 unt; 0 nHn; 49 RR)
% Number of literals : 119 ( 0 equ; 76 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aElement0(sz10),
file('RNG097+1.p',unknown),
[] ).
cnf(3,axiom,
aIdeal0(xI),
file('RNG097+1.p',unknown),
[] ).
cnf(4,axiom,
aIdeal0(xJ),
file('RNG097+1.p',unknown),
[] ).
cnf(5,axiom,
aElement0(xx),
file('RNG097+1.p',unknown),
[] ).
cnf(8,axiom,
aElementOf0(xa,xI),
file('RNG097+1.p',unknown),
[] ).
cnf(9,axiom,
aElementOf0(xb,xJ),
file('RNG097+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ aIdeal0(u)
| aSet0(u) ),
file('RNG097+1.p',unknown),
[] ).
cnf(12,axiom,
equal(sdtpldt0(xa,xb),sz10),
file('RNG097+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ aElement0(u)
| aElement0(smndt0(u)) ),
file('RNG097+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('RNG097+1.p',unknown),
[] ).
cnf(22,axiom,
~ aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
file('RNG097+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('RNG097+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('RNG097+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG097+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(smndt0(sz10),u),smndt0(u)) ),
file('RNG097+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('RNG097+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aIdeal0(u)
| ~ aElement0(v)
| ~ aElementOf0(w,u)
| aElementOf0(sdtasdt0(v,w),u) ),
file('RNG097+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('RNG097+1.p',unknown),
[] ).
cnf(67,plain,
( ~ aElement0(xx)
| ~ aIdeal0(xI)
| ~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI) ),
inference(res,[status(thm),theory(equality)],[41,22]),
[iquote('0:Res:41.3,22.0')] ).
cnf(71,plain,
~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI),
inference(mrr,[status(thm)],[67,5,3]),
[iquote('0:MRR:67.0,67.1,5.0,3.0')] ).
cnf(94,plain,
( ~ aSet0(xJ)
| aElement0(xb) ),
inference(res,[status(thm),theory(equality)],[9,25]),
[iquote('0:Res:9.0,25.1')] ).
cnf(95,plain,
( ~ aSet0(xI)
| aElement0(xa) ),
inference(res,[status(thm),theory(equality)],[8,25]),
[iquote('0:Res:8.0,25.1')] ).
cnf(99,plain,
aElement0(xb),
inference(ssi,[status(thm)],[94,11,4]),
[iquote('0:SSi:94.0,11.0,4.1')] ).
cnf(100,plain,
aElement0(xa),
inference(ssi,[status(thm)],[95,11,3]),
[iquote('0:SSi:95.0,11.0,3.1')] ).
cnf(201,plain,
( ~ aElement0(u)
| ~ aIdeal0(v)
| ~ aElement0(smndt0(sz10))
| ~ aElementOf0(u,v)
| aElementOf0(smndt0(u),v) ),
inference(spr,[status(thm),theory(equality)],[31,41]),
[iquote('0:SpR:31.1,41.3')] ).
cnf(212,plain,
( ~ aElement0(u)
| ~ aIdeal0(v)
| ~ aElementOf0(u,v)
| aElementOf0(smndt0(u),v) ),
inference(ssi,[status(thm)],[201,13,2]),
[iquote('0:SSi:201.2,13.0,2.1')] ).
cnf(503,plain,
( ~ aElement0(u)
| ~ aElement0(xb)
| ~ aElement0(xa)
| equal(sdtpldt0(xa,sdtpldt0(xb,u)),sdtpldt0(sz10,u)) ),
inference(spr,[status(thm),theory(equality)],[12,56]),
[iquote('0:SpR:12.0,56.3')] ).
cnf(505,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)],[24,56]),
[iquote('0:SpR:24.1,56.3')] ).
cnf(508,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)],[23,56]),
[iquote('0:SpR:23.1,56.3')] ).
cnf(518,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xa,sdtpldt0(xb,u)),sdtpldt0(sz10,u)) ),
inference(ssi,[status(thm)],[503,100,99]),
[iquote('0:SSi:503.2,503.1,100.0,99.0')] ).
cnf(523,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[508]),
[iquote('0:Obv:508.0')] ).
cnf(524,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[15,523]),
[iquote('0:Rew:15.1,523.3')] ).
cnf(525,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[524,13]),
[iquote('0:SSi:524.1,13.1')] ).
cnf(526,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[505]),
[iquote('0:Obv:505.0')] ).
cnf(527,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[15,526]),
[iquote('0:Rew:15.1,526.3')] ).
cnf(528,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[527,13]),
[iquote('0:SSi:527.2,13.1')] ).
cnf(710,plain,
( ~ aElement0(u)
| ~ aElement0(xb)
| ~ aElement0(u)
| equal(sdtpldt0(xa,sdtpldt0(u,xb)),sdtpldt0(sz10,u)) ),
inference(spr,[status(thm),theory(equality)],[37,518]),
[iquote('0:SpR:37.2,518.1')] ).
cnf(719,plain,
( ~ aElement0(xb)
| ~ aElement0(u)
| equal(sdtpldt0(xa,sdtpldt0(u,xb)),sdtpldt0(sz10,u)) ),
inference(obv,[status(thm),theory(equality)],[710]),
[iquote('0:Obv:710.0')] ).
cnf(720,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xa,sdtpldt0(u,xb)),sdtpldt0(sz10,u)) ),
inference(ssi,[status(thm)],[719,99]),
[iquote('0:SSi:719.0,99.0')] ).
cnf(1672,plain,
( ~ aElement0(xb)
| ~ aElement0(xa)
| ~ aElement0(smndt0(xa))
| equal(sdtpldt0(sz10,smndt0(xa)),xb) ),
inference(spr,[status(thm),theory(equality)],[525,720]),
[iquote('0:SpR:525.2,720.1')] ).
cnf(1699,plain,
equal(sdtpldt0(sz10,smndt0(xa)),xb),
inference(ssi,[status(thm)],[1672,13,100,99]),
[iquote('0:SSi:1672.2,1672.1,1672.0,13.0,100.0,100.0,99.1')] ).
cnf(1812,plain,
( ~ aElement0(smndt0(xa))
| ~ aElement0(sz10)
| equal(sdtpldt0(smndt0(sz10),xb),smndt0(xa)) ),
inference(spr,[status(thm),theory(equality)],[1699,528]),
[iquote('0:SpR:1699.0,528.2')] ).
cnf(1825,plain,
equal(sdtpldt0(smndt0(sz10),xb),smndt0(xa)),
inference(ssi,[status(thm)],[1812,2,13,100]),
[iquote('0:SSi:1812.1,1812.0,2.0,13.1,100.0')] ).
cnf(2152,plain,
( ~ aElement0(xb)
| ~ aElement0(smndt0(sz10))
| equal(sdtpldt0(xb,smndt0(sz10)),smndt0(xa)) ),
inference(spr,[status(thm),theory(equality)],[1825,37]),
[iquote('0:SpR:1825.0,37.2')] ).
cnf(2165,plain,
equal(sdtpldt0(xb,smndt0(sz10)),smndt0(xa)),
inference(ssi,[status(thm)],[2152,13,2,99]),
[iquote('0:SSi:2152.1,2152.0,13.0,2.0,99.1')] ).
cnf(2166,plain,
~ aElementOf0(smndt0(xa),xI),
inference(rew,[status(thm),theory(equality)],[2165,71]),
[iquote('0:Rew:2165.0,71.0')] ).
cnf(2191,plain,
( ~ aElement0(xa)
| ~ aIdeal0(xI)
| ~ aElementOf0(xa,xI) ),
inference(res,[status(thm),theory(equality)],[212,2166]),
[iquote('0:Res:212.3,2166.0')] ).
cnf(2192,plain,
~ aElementOf0(xa,xI),
inference(ssi,[status(thm)],[2191,3,100]),
[iquote('0:SSi:2191.1,2191.0,3.0,100.0')] ).
cnf(2193,plain,
$false,
inference(mrr,[status(thm)],[2192,8]),
[iquote('0:MRR:2192.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG097+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 18:01:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.69/0.89
% 0.69/0.89 SPASS V 3.9
% 0.69/0.89 SPASS beiseite: Proof found.
% 0.69/0.89 % SZS status Theorem
% 0.69/0.89 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.89 SPASS derived 1380 clauses, backtracked 0 clauses, performed 0 splits and kept 662 clauses.
% 0.69/0.89 SPASS allocated 100015 KBytes.
% 0.69/0.89 SPASS spent 0:00:00.51 on the problem.
% 0.69/0.89 0:00:00.04 for the input.
% 0.69/0.89 0:00:00.10 for the FLOTTER CNF translation.
% 0.69/0.89 0:00:00.02 for inferences.
% 0.69/0.89 0:00:00.00 for the backtracking.
% 0.69/0.89 0:00:00.32 for the reduction.
% 0.69/0.89
% 0.69/0.89
% 0.69/0.89 Here is a proof with depth 5, length 49 :
% 0.69/0.89 % SZS output start Refutation
% See solution above
% 0.69/0.89 Formulae used in the proof : mSortsC_01 m__1205 m__1217 m__1294 mDefIdeal mSortsU mAddZero m__ mAddInvr mEOfElem mMulMnOne mAddComm mAddAsso
% 0.69/0.89
%------------------------------------------------------------------------------