TSTP Solution File: RNG122+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG122+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 20:41:32 EDT 2022
% Result : Theorem 0.92s 1.11s
% Output : Refutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 34 ( 16 unt; 0 nHn; 34 RR)
% Number of literals : 65 ( 0 equ; 39 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
aElement0(xb),
file('RNG122+1.p',unknown),
[] ).
cnf(5,axiom,
aIdeal0(xI),
file('RNG122+1.p',unknown),
[] ).
cnf(8,axiom,
aElement0(xq),
file('RNG122+1.p',unknown),
[] ).
cnf(9,axiom,
aElement0(xr),
file('RNG122+1.p',unknown),
[] ).
cnf(11,axiom,
aElementOf0(xu,xI),
file('RNG122+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ aIdeal0(u)
| aSet0(u) ),
file('RNG122+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ aElement0(u)
| aElement0(smndt0(u)) ),
file('RNG122+1.p',unknown),
[] ).
cnf(36,axiom,
equal(sdtpldt0(sdtasdt0(xq,xu),xr),xb),
file('RNG122+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('RNG122+1.p',unknown),
[] ).
cnf(47,axiom,
~ equal(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),xr),
file('RNG122+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('RNG122+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG122+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(sdtasdt0(v,u)) ),
file('RNG122+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('RNG122+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('RNG122+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ aElement0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('RNG122+1.p',unknown),
[] ).
cnf(144,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(res,[status(thm),theory(equality)],[11,50]),
[iquote('0:Res:11.0,50.1')] ).
cnf(153,plain,
aElement0(xu),
inference(ssi,[status(thm)],[144,29,5]),
[iquote('0:SSi:144.0,29.0,5.1')] ).
cnf(191,plain,
( ~ aElement0(xu)
| ~ aElement0(xq)
| equal(sdtpldt0(sdtasdt0(xu,xq),xr),xb) ),
inference(spr,[status(thm),theory(equality)],[69,36]),
[iquote('0:SpR:69.2,36.0')] ).
cnf(213,plain,
( ~ aElement0(xu)
| ~ aElement0(xq)
| ~ equal(sdtpldt0(smndt0(sdtasdt0(xu,xq)),xb),xr) ),
inference(spl,[status(thm),theory(equality)],[69,47]),
[iquote('0:SpL:69.2,47.0')] ).
cnf(217,plain,
equal(sdtpldt0(sdtasdt0(xu,xq),xr),xb),
inference(ssi,[status(thm)],[191,8,153]),
[iquote('0:SSi:191.1,191.0,8.0,153.0')] ).
cnf(226,plain,
~ equal(sdtpldt0(smndt0(sdtasdt0(xu,xq)),xb),xr),
inference(ssi,[status(thm)],[213,8,153]),
[iquote('0:SSi:213.1,213.0,8.0,153.0')] ).
cnf(237,plain,
( ~ aElement0(xr)
| ~ aElement0(sdtasdt0(xu,xq))
| equal(sdtpldt0(xr,sdtasdt0(xu,xq)),xb) ),
inference(spr,[status(thm),theory(equality)],[68,217]),
[iquote('0:SpR:68.2,217.0')] ).
cnf(259,plain,
equal(sdtpldt0(xr,sdtasdt0(xu,xq)),xb),
inference(ssi,[status(thm)],[237,57,153,8,9]),
[iquote('0:SSi:237.1,237.0,57.0,153.0,8.0,9.2')] ).
cnf(271,plain,
( ~ aElement0(xb)
| ~ aElement0(smndt0(sdtasdt0(xu,xq)))
| ~ equal(sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))),xr) ),
inference(spl,[status(thm),theory(equality)],[68,226]),
[iquote('0:SpL:68.2,226.0')] ).
cnf(273,plain,
~ equal(sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))),xr),
inference(ssi,[status(thm)],[271,30,57,153,8,4]),
[iquote('0:SSi:271.1,271.0,30.0,57.0,153.0,8.2,4.1')] ).
cnf(841,plain,
( ~ aElement0(u)
| ~ aElement0(sdtasdt0(xu,xq))
| ~ aElement0(xr)
| equal(sdtpldt0(xr,sdtpldt0(sdtasdt0(xu,xq),u)),sdtpldt0(xb,u)) ),
inference(spr,[status(thm),theory(equality)],[259,98]),
[iquote('0:SpR:259.0,98.3')] ).
cnf(853,plain,
( ~ aElement0(u)
| equal(sdtpldt0(xr,sdtpldt0(sdtasdt0(xu,xq),u)),sdtpldt0(xb,u)) ),
inference(ssi,[status(thm)],[841,9,57,153,8]),
[iquote('0:SSi:841.2,841.1,9.0,57.0,153.2,8.0')] ).
cnf(2668,plain,
( ~ aElement0(sdtasdt0(xu,xq))
| ~ aElement0(smndt0(sdtasdt0(xu,xq)))
| equal(sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))),sdtpldt0(xr,sz00)) ),
inference(spr,[status(thm),theory(equality)],[48,853]),
[iquote('0:SpR:48.1,853.1')] ).
cnf(2675,plain,
equal(sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))),sdtpldt0(xr,sz00)),
inference(ssi,[status(thm)],[2668,30,57,153,8]),
[iquote('0:SSi:2668.1,2668.0,30.0,57.0,153.2,8.0,57.0,153.2,8.1')] ).
cnf(2676,plain,
~ equal(sdtpldt0(xr,sz00),xr),
inference(rew,[status(thm),theory(equality)],[2675,273]),
[iquote('0:Rew:2675.0,273.0')] ).
cnf(2731,plain,
( ~ aElement0(xr)
| ~ equal(xr,xr) ),
inference(spl,[status(thm),theory(equality)],[37,2676]),
[iquote('0:SpL:37.1,2676.0')] ).
cnf(2732,plain,
~ aElement0(xr),
inference(obv,[status(thm),theory(equality)],[2731]),
[iquote('0:Obv:2731.1')] ).
cnf(2733,plain,
$false,
inference(ssi,[status(thm)],[2732,9]),
[iquote('0:SSi:2732.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG122+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 21:49:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.92/1.11
% 0.92/1.11 SPASS V 3.9
% 0.92/1.11 SPASS beiseite: Proof found.
% 0.92/1.11 % SZS status Theorem
% 0.92/1.11 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.11 SPASS derived 1593 clauses, backtracked 0 clauses, performed 0 splits and kept 685 clauses.
% 0.92/1.11 SPASS allocated 100792 KBytes.
% 0.92/1.11 SPASS spent 0:00:00.73 on the problem.
% 0.92/1.11 0:00:00.04 for the input.
% 0.92/1.11 0:00:00.15 for the FLOTTER CNF translation.
% 0.92/1.11 0:00:00.04 for inferences.
% 0.92/1.11 0:00:00.00 for the backtracking.
% 0.92/1.11 0:00:00.46 for the reduction.
% 0.92/1.11
% 0.92/1.11
% 0.92/1.11 Here is a proof with depth 4, length 34 :
% 0.92/1.11 % SZS output start Refutation
% See solution above
% 0.92/1.11 Formulae used in the proof : m__2091 m__2174 m__2666 m__2273 mDefIdeal mSortsU mAddZero m__ mAddInvr mEOfElem mSortsB_02 mAddComm mMulComm mAddAsso
% 0.92/1.11
%------------------------------------------------------------------------------