TSTP Solution File: RNG097+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG097+2 : 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 20:41:28 EDT 2022
% Result : Theorem 0.75s 0.92s
% Output : Refutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of clauses : 50 ( 19 unt; 0 nHn; 50 RR)
% Number of literals : 114 ( 0 equ; 70 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+2.p',unknown),
[] ).
cnf(3,axiom,
aSet0(xI),
file('RNG097+2.p',unknown),
[] ).
cnf(4,axiom,
aIdeal0(xI),
file('RNG097+2.p',unknown),
[] ).
cnf(5,axiom,
aSet0(xJ),
file('RNG097+2.p',unknown),
[] ).
cnf(6,axiom,
aIdeal0(xJ),
file('RNG097+2.p',unknown),
[] ).
cnf(7,axiom,
aElement0(xx),
file('RNG097+2.p',unknown),
[] ).
cnf(10,axiom,
aElementOf0(xa,xI),
file('RNG097+2.p',unknown),
[] ).
cnf(11,axiom,
aElementOf0(xb,xJ),
file('RNG097+2.p',unknown),
[] ).
cnf(16,axiom,
equal(sdtpldt0(xa,xb),sz10),
file('RNG097+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ aElement0(u)
| aElement0(smndt0(u)) ),
file('RNG097+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('RNG097+2.p',unknown),
[] ).
cnf(26,axiom,
~ aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
file('RNG097+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('RNG097+2.p',unknown),
[] ).
cnf(28,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('RNG097+2.p',unknown),
[] ).
cnf(29,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG097+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(smndt0(sz10),u),smndt0(u)) ),
file('RNG097+2.p',unknown),
[] ).
cnf(42,axiom,
( ~ aElement0(u)
| ~ aElementOf0(v,xI)
| aElementOf0(sdtasdt0(u,v),xI) ),
file('RNG097+2.p',unknown),
[] ).
cnf(44,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('RNG097+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('RNG097+2.p',unknown),
[] ).
cnf(75,plain,
( ~ aElement0(xx)
| ~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI) ),
inference(res,[status(thm),theory(equality)],[42,26]),
[iquote('0:Res:42.2,26.0')] ).
cnf(81,plain,
~ aElementOf0(sdtpldt0(xb,smndt0(sz10)),xI),
inference(mrr,[status(thm)],[75,7]),
[iquote('0:MRR:75.0,7.0')] ).
cnf(106,plain,
( ~ aSet0(xJ)
| aElement0(xb) ),
inference(res,[status(thm),theory(equality)],[11,29]),
[iquote('0:Res:11.0,29.1')] ).
cnf(108,plain,
( ~ aSet0(xI)
| aElement0(xa) ),
inference(res,[status(thm),theory(equality)],[10,29]),
[iquote('0:Res:10.0,29.1')] ).
cnf(113,plain,
aElement0(xb),
inference(ssi,[status(thm)],[106,6,5]),
[iquote('0:SSi:106.0,6.0,5.0')] ).
cnf(114,plain,
aElement0(xa),
inference(ssi,[status(thm)],[108,4,3]),
[iquote('0:SSi:108.0,4.0,3.0')] ).
cnf(163,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(sz10))
| ~ aElementOf0(u,xI)
| aElementOf0(smndt0(u),xI) ),
inference(spr,[status(thm),theory(equality)],[35,42]),
[iquote('0:SpR:35.1,42.2')] ).
cnf(172,plain,
( ~ aElement0(u)
| ~ aElementOf0(u,xI)
| aElementOf0(smndt0(u),xI) ),
inference(ssi,[status(thm)],[163,17,2]),
[iquote('0:SSi:163.1,17.0,2.1')] ).
cnf(795,plain,
( ~ aElement0(u)
| ~ aElement0(xb)
| ~ aElement0(xa)
| equal(sdtpldt0(xa,sdtpldt0(xb,u)),sdtpldt0(sz10,u)) ),
inference(spr,[status(thm),theory(equality)],[16,65]),
[iquote('0:SpR:16.0,65.3')] ).
cnf(797,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)],[28,65]),
[iquote('0:SpR:28.1,65.3')] ).
cnf(800,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)],[27,65]),
[iquote('0:SpR:27.1,65.3')] ).
cnf(810,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xa,sdtpldt0(xb,u)),sdtpldt0(sz10,u)) ),
inference(ssi,[status(thm)],[795,114,113]),
[iquote('0:SSi:795.2,795.1,114.0,113.0')] ).
cnf(815,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[800]),
[iquote('0:Obv:800.0')] ).
cnf(816,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(v))
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[19,815]),
[iquote('0:Rew:19.1,815.3')] ).
cnf(817,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[816,17]),
[iquote('0:SSi:816.1,17.1')] ).
cnf(818,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[797]),
[iquote('0:Obv:797.0')] ).
cnf(819,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[19,818]),
[iquote('0:Rew:19.1,818.3')] ).
cnf(820,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[819,17]),
[iquote('0:SSi:819.2,17.1')] ).
cnf(1013,plain,
( ~ aElement0(u)
| ~ aElement0(xb)
| ~ aElement0(u)
| equal(sdtpldt0(xa,sdtpldt0(u,xb)),sdtpldt0(sz10,u)) ),
inference(spr,[status(thm),theory(equality)],[44,810]),
[iquote('0:SpR:44.2,810.1')] ).
cnf(1023,plain,
( ~ aElement0(xb)
| ~ aElement0(u)
| equal(sdtpldt0(xa,sdtpldt0(u,xb)),sdtpldt0(sz10,u)) ),
inference(obv,[status(thm),theory(equality)],[1013]),
[iquote('0:Obv:1013.0')] ).
cnf(1024,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xa,sdtpldt0(u,xb)),sdtpldt0(sz10,u)) ),
inference(ssi,[status(thm)],[1023,113]),
[iquote('0:SSi:1023.0,113.0')] ).
cnf(2099,plain,
( ~ aElement0(xb)
| ~ aElement0(xa)
| ~ aElement0(smndt0(xa))
| equal(sdtpldt0(sz10,smndt0(xa)),xb) ),
inference(spr,[status(thm),theory(equality)],[817,1024]),
[iquote('0:SpR:817.2,1024.1')] ).
cnf(2126,plain,
equal(sdtpldt0(sz10,smndt0(xa)),xb),
inference(ssi,[status(thm)],[2099,17,114,113]),
[iquote('0:SSi:2099.2,2099.1,2099.0,17.0,114.0,114.0,113.1')] ).
cnf(2249,plain,
( ~ aElement0(smndt0(xa))
| ~ aElement0(sz10)
| equal(sdtpldt0(smndt0(sz10),xb),smndt0(xa)) ),
inference(spr,[status(thm),theory(equality)],[2126,820]),
[iquote('0:SpR:2126.0,820.2')] ).
cnf(2264,plain,
equal(sdtpldt0(smndt0(sz10),xb),smndt0(xa)),
inference(ssi,[status(thm)],[2249,2,17,114]),
[iquote('0:SSi:2249.1,2249.0,2.0,17.1,114.0')] ).
cnf(2626,plain,
( ~ aElement0(xb)
| ~ aElement0(smndt0(sz10))
| equal(sdtpldt0(xb,smndt0(sz10)),smndt0(xa)) ),
inference(spr,[status(thm),theory(equality)],[2264,44]),
[iquote('0:SpR:2264.0,44.2')] ).
cnf(2644,plain,
equal(sdtpldt0(xb,smndt0(sz10)),smndt0(xa)),
inference(ssi,[status(thm)],[2626,17,2,113]),
[iquote('0:SSi:2626.1,2626.0,17.0,2.0,113.1')] ).
cnf(2645,plain,
~ aElementOf0(smndt0(xa),xI),
inference(rew,[status(thm),theory(equality)],[2644,81]),
[iquote('0:Rew:2644.0,81.0')] ).
cnf(2667,plain,
( ~ aElement0(xa)
| ~ aElementOf0(xa,xI) ),
inference(res,[status(thm),theory(equality)],[172,2645]),
[iquote('0:Res:172.2,2645.0')] ).
cnf(2670,plain,
~ aElementOf0(xa,xI),
inference(ssi,[status(thm)],[2667,114]),
[iquote('0:SSi:2667.0,114.0')] ).
cnf(2671,plain,
$false,
inference(mrr,[status(thm)],[2670,10]),
[iquote('0:MRR:2670.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG097+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % 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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 06:37:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/0.92
% 0.75/0.92 SPASS V 3.9
% 0.75/0.92 SPASS beiseite: Proof found.
% 0.75/0.92 % SZS status Theorem
% 0.75/0.92 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.75/0.92 SPASS derived 1782 clauses, backtracked 0 clauses, performed 0 splits and kept 729 clauses.
% 0.75/0.92 SPASS allocated 100299 KBytes.
% 0.75/0.92 SPASS spent 0:00:00.55 on the problem.
% 0.75/0.92 0:00:00.04 for the input.
% 0.75/0.92 0:00:00.09 for the FLOTTER CNF translation.
% 0.75/0.92 0:00:00.03 for inferences.
% 0.75/0.92 0:00:00.00 for the backtracking.
% 0.75/0.92 0:00:00.37 for the reduction.
% 0.75/0.92
% 0.75/0.92
% 0.75/0.92 Here is a proof with depth 5, length 50 :
% 0.75/0.92 % SZS output start Refutation
% See solution above
% 0.75/0.92 Formulae used in the proof : mSortsC_01 m__1205 m__1217 m__1294 mSortsU mAddZero m__ mAddInvr mEOfElem mMulMnOne mAddComm mAddAsso
% 0.75/0.92
%------------------------------------------------------------------------------