%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG083+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of clauses : 37 ( 6 unt; 0 nHn; 37 RR)
% Number of literals : 106 ( 0 equ; 75 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aElement0(sz00),
file('RNG083+1.p',unknown),
[] ).
cnf(3,axiom,
aElement0(xx),
file('RNG083+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ aElement0(u)
| aElement0(smndt0(u)) ),
file('RNG083+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('RNG083+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('RNG083+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtasdt0(v,u)) ),
file('RNG083+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ equal(sdtasdt0(sz00,xx),sz00)
| ~ equal(sdtasdt0(xx,sz00),sz00) ),
file('RNG083+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('RNG083+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('RNG083+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('RNG083+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtasdt0(sdtpldt0(v,u),w),sdtpldt0(sdtasdt0(v,w),sdtasdt0(u,w))) ),
file('RNG083+1.p',unknown),
[] ).
cnf(74,plain,
( ~ aElement0(sz00)
| ~ aElement0(xx)
| ~ equal(sdtasdt0(sz00,xx),sz00)
| ~ equal(sdtasdt0(sz00,xx),sz00) ),
inference(spl,[status(thm),theory(equality)],[17,15]),
[iquote('0:SpL:17.2,15.1')] ).
cnf(86,plain,
( ~ aElement0(sz00)
| ~ aElement0(xx)
| ~ equal(sdtasdt0(sz00,xx),sz00) ),
inference(obv,[status(thm),theory(equality)],[74]),
[iquote('0:Obv:74.2')] ).
cnf(87,plain,
~ equal(sdtasdt0(sz00,xx),sz00),
inference(ssi,[status(thm)],[86,3,1]),
[iquote('0:SSi:86.1,86.0,3.0,1.0')] ).
cnf(116,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(u)
| ~ aElement0(sz00)
| equal(sdtpldt0(sz00,sdtpldt0(u,v)),sdtpldt0(u,v)) ),
inference(spr,[status(thm),theory(equality)],[6,19]),
[iquote('0:SpR:6.1,19.3')] ).
cnf(117,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)],[10,19]),
[iquote('0:SpR:10.1,19.3')] ).
cnf(124,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(sz00)
| equal(sdtpldt0(sz00,sdtpldt0(v,u)),sdtpldt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[116]),
[iquote('0:Obv:116.0')] ).
cnf(125,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(sz00,sdtpldt0(v,u)),sdtpldt0(v,u)) ),
inference(ssi,[status(thm)],[124,1]),
[iquote('0:SSi:124.2,1.0')] ).
cnf(129,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[117]),
[iquote('0:Obv:117.0')] ).
cnf(130,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[6,129]),
[iquote('0:Rew:6.1,129.3')] ).
cnf(131,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[130,4]),
[iquote('0:SSi:130.2,4.1')] ).
cnf(187,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(v)
| ~ aElement0(u)
| equal(sdtpldt0(smndt0(u),sdtpldt0(v,u)),v) ),
inference(spr,[status(thm),theory(equality)],[16,131]),
[iquote('0:SpR:16.2,131.2')] ).
cnf(198,plain,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(u,v)),u) ),
inference(obv,[status(thm),theory(equality)],[187]),
[iquote('0:Obv:187.1')] ).
cnf(333,plain,
( ~ aElement0(u)
| ~ aElement0(u)
| ~ aElement0(smndt0(u))
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(spr,[status(thm),theory(equality)],[10,125]),
[iquote('0:SpR:10.1,125.2')] ).
cnf(345,plain,
( ~ aElement0(u)
| ~ aElement0(smndt0(u))
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(obv,[status(thm),theory(equality)],[333]),
[iquote('0:Obv:333.0')] ).
cnf(346,plain,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,sz00),sz00) ),
inference(ssi,[status(thm)],[345,4]),
[iquote('0:SSi:345.1,4.1')] ).
cnf(362,plain,
equal(sdtpldt0(sz00,sz00),sz00),
inference(ems,[status(thm)],[346,1]),
[iquote('0:EmS:346.0,1.0')] ).
cnf(402,plain,
( ~ aElement0(sz00)
| ~ aElement0(sz00)
| ~ aElement0(u)
| equal(sdtpldt0(sdtasdt0(sz00,u),sdtasdt0(sz00,u)),sdtasdt0(sz00,u)) ),
inference(spr,[status(thm),theory(equality)],[362,20]),
[iquote('0:SpR:362.0,20.3')] ).
cnf(403,plain,
( ~ aElement0(sz00)
| ~ aElement0(u)
| equal(sdtpldt0(sdtasdt0(sz00,u),sdtasdt0(sz00,u)),sdtasdt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[402]),
[iquote('0:Obv:402.0')] ).
cnf(404,plain,
( ~ aElement0(u)
| equal(sdtpldt0(sdtasdt0(sz00,u),sdtasdt0(sz00,u)),sdtasdt0(sz00,u)) ),
inference(ssi,[status(thm)],[403,1]),
[iquote('0:SSi:403.0,1.0')] ).
cnf(450,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(sz00,u))
| ~ aElement0(sdtasdt0(sz00,u))
| equal(sdtpldt0(smndt0(sdtasdt0(sz00,u)),sdtasdt0(sz00,u)),sdtasdt0(sz00,u)) ),
inference(spr,[status(thm),theory(equality)],[404,198]),
[iquote('0:SpR:404.1,198.2')] ).
cnf(471,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(sz00,u))
| equal(sdtpldt0(smndt0(sdtasdt0(sz00,u)),sdtasdt0(sz00,u)),sdtasdt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[450]),
[iquote('0:Obv:450.1')] ).
cnf(472,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(sz00,u))
| equal(sdtasdt0(sz00,u),sz00) ),
inference(rew,[status(thm),theory(equality)],[10,471]),
[iquote('0:Rew:10.1,471.2')] ).
cnf(473,plain,
( ~ aElement0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
inference(ssi,[status(thm)],[472,12,1]),
[iquote('0:SSi:472.1,12.0,1.2')] ).
cnf(494,plain,
( ~ aElement0(xx)
| ~ equal(sz00,sz00) ),
inference(spl,[status(thm),theory(equality)],[473,87]),
[iquote('0:SpL:473.1,87.0')] ).
cnf(495,plain,
~ aElement0(xx),
inference(obv,[status(thm),theory(equality)],[494]),
[iquote('0:Obv:494.1')] ).
cnf(496,plain,
$false,
inference(ssi,[status(thm)],[495,3]),
[iquote('0:SSi:495.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG083+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 22:29:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 242 clauses, backtracked 0 clauses, performed 0 splits and kept 85 clauses.
% 0.20/0.47 SPASS allocated 104381 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.03 for the input.
% 0.20/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.04 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 6, length 37 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : mSortsC m__468 mSortsU mAddZero mAddInvr mSortsB_02 m__ mAddComm mMulComm mAddAsso mAMDistr
% 0.20/0.47
%------------------------------------------------------------------------------