TSTP Solution File: RNG098+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG098+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 0.10s 0.57s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of clauses : 27 ( 15 unt; 0 nHn; 27 RR)
% Number of literals : 49 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aElement0(sz10),
file('RNG098+2.p',unknown),
[] ).
cnf(5,axiom,
aSet0(xJ),
file('RNG098+2.p',unknown),
[] ).
cnf(6,axiom,
aIdeal0(xJ),
file('RNG098+2.p',unknown),
[] ).
cnf(7,axiom,
aElement0(xx),
file('RNG098+2.p',unknown),
[] ).
cnf(8,axiom,
aElement0(xy),
file('RNG098+2.p',unknown),
[] ).
cnf(10,axiom,
aElementOf0(xa,xI),
file('RNG098+2.p',unknown),
[] ).
cnf(11,axiom,
aElementOf0(xb,xJ),
file('RNG098+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ aElement0(u)
| aElement0(smndt0(u)) ),
file('RNG098+2.p',unknown),
[] ).
cnf(18,axiom,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('RNG098+2.p',unknown),
[] ).
cnf(27,axiom,
aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI),
file('RNG098+2.p',unknown),
[] ).
cnf(30,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG098+2.p',unknown),
[] ).
cnf(37,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
file('RNG098+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ aElement0(u)
| ~ aElementOf0(v,xI)
| aElementOf0(sdtasdt0(u,v),xI) ),
file('RNG098+2.p',unknown),
[] ).
cnf(47,axiom,
( ~ aElementOf0(u,xI)
| ~ aElementOf0(v,xI)
| aElementOf0(sdtpldt0(u,v),xI) ),
file('RNG098+2.p',unknown),
[] ).
cnf(52,axiom,
equal(sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))),sdtpldt0(xw,smndt0(xx))),
file('RNG098+2.p',unknown),
[] ).
cnf(69,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u))) ),
file('RNG098+2.p',unknown),
[] ).
cnf(108,plain,
( ~ aSet0(xJ)
| aElement0(xb) ),
inference(res,[status(thm),theory(equality)],[11,30]),
[iquote('0:Res:11.0,30.1')] ).
cnf(116,plain,
aElement0(xb),
inference(ssi,[status(thm)],[108,6,5]),
[iquote('0:SSi:108.0,6.0,5.0')] ).
cnf(363,plain,
( ~ aElementOf0(sdtasdt0(xy,xa),xI)
| ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI)
| aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ),
inference(spr,[status(thm),theory(equality)],[52,47]),
[iquote('0:SpR:52.0,47.2')] ).
cnf(371,plain,
( ~ aElementOf0(sdtasdt0(xy,xa),xI)
| ~ aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI) ),
inference(mrr,[status(thm)],[363,18]),
[iquote('0:MRR:363.2,18.0')] ).
cnf(1339,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(xb)
| ~ aElement0(xx)
| aElementOf0(sdtpldt0(sdtasdt0(xx,xb),sdtasdt0(xx,smndt0(sz10))),xI) ),
inference(spr,[status(thm),theory(equality)],[69,27]),
[iquote('0:SpR:69.3,27.0')] ).
cnf(1387,plain,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(xb)
| ~ aElement0(xx)
| aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI) ),
inference(rew,[status(thm),theory(equality)],[37,1339]),
[iquote('0:Rew:37.1,1339.3')] ).
cnf(1388,plain,
aElementOf0(sdtpldt0(sdtasdt0(xx,xb),smndt0(xx)),xI),
inference(ssi,[status(thm)],[1387,7,116,17,2]),
[iquote('0:SSi:1387.2,1387.1,1387.0,7.0,116.1,17.0,2.0')] ).
cnf(1389,plain,
~ aElementOf0(sdtasdt0(xy,xa),xI),
inference(mrr,[status(thm)],[371,1388]),
[iquote('0:MRR:371.1,1388.0')] ).
cnf(1448,plain,
( ~ aElement0(xy)
| ~ aElementOf0(xa,xI) ),
inference(res,[status(thm),theory(equality)],[43,1389]),
[iquote('0:Res:43.2,1389.0')] ).
cnf(1450,plain,
~ aElementOf0(xa,xI),
inference(ssi,[status(thm)],[1448,8]),
[iquote('0:SSi:1448.0,8.0')] ).
cnf(1451,plain,
$false,
inference(mrr,[status(thm)],[1450,10]),
[iquote('0:MRR:1450.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : RNG098+2 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.06/0.25 % Computer : n025.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Mon May 30 10:26:27 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.10/0.57
% 0.10/0.57 SPASS V 3.9
% 0.10/0.57 SPASS beiseite: Proof found.
% 0.10/0.57 % SZS status Theorem
% 0.10/0.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.57 SPASS derived 919 clauses, backtracked 0 clauses, performed 0 splits and kept 402 clauses.
% 0.10/0.57 SPASS allocated 99165 KBytes.
% 0.10/0.57 SPASS spent 0:00:00.29 on the problem.
% 0.10/0.57 0:00:00.03 for the input.
% 0.10/0.57 0:00:00.10 for the FLOTTER CNF translation.
% 0.10/0.57 0:00:00.01 for inferences.
% 0.10/0.57 0:00:00.00 for the backtracking.
% 0.10/0.57 0:00:00.13 for the reduction.
% 0.10/0.57
% 0.10/0.57
% 0.10/0.57 Here is a proof with depth 2, length 27 :
% 0.10/0.57 % SZS output start Refutation
% See solution above
% 0.10/0.57 Formulae used in the proof : mSortsC_01 m__1205 m__1217 m__1294 mSortsU m__ m__1393 mEOfElem mMulMnOne m__1374 mAMDistr
% 0.10/0.57
%------------------------------------------------------------------------------