TSTP Solution File: RNG106+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG106+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 20:41:29 EDT 2022
% Result : Theorem 4.19s 4.44s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 7 unt; 4 nHn; 24 RR)
% Number of literals : 60 ( 0 equ; 37 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aElement0(xc),
file('RNG106+1.p',unknown),
[] ).
cnf(4,axiom,
aElement0(skf28(u)),
file('RNG106+1.p',unknown),
[] ).
cnf(5,axiom,
~ aIdeal0(slsdtgt0(xc)),
file('RNG106+1.p',unknown),
[] ).
cnf(13,axiom,
aElement0(skf19(u,v,w)),
file('RNG106+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aSet0(u)
| aIdeal0(u)
| aElementOf0(skf26(u),u) ),
file('RNG106+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aElement0(u)
| ~ equal(v,slsdtgt0(u))
| aSet0(v) ),
file('RNG106+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ aElement0(u)
| ~ aElementOf0(v,slsdtgt0(xc))
| aElementOf0(sdtasdt0(u,v),slsdtgt0(xc)) ),
file('RNG106+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sdtasdt0(skf28(u),skf26(u)),u)
| aIdeal0(u)
| aElementOf0(skf27(u),u) ),
file('RNG106+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ aElement0(u)
| ~ aElementOf0(v,slsdtgt0(xc))
| ~ aElementOf0(w,slsdtgt0(xc))
| aElementOf0(sdtpldt0(w,v),slsdtgt0(xc)) ),
file('RNG106+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sdtpldt0(skf26(u),skf27(u)),u)
| ~ aElementOf0(sdtasdt0(skf28(u),skf26(u)),u)
| aIdeal0(u) ),
file('RNG106+1.p',unknown),
[] ).
cnf(116,plain,
( ~ aElementOf0(u,slsdtgt0(xc))
| ~ aElementOf0(v,slsdtgt0(xc))
| aElementOf0(sdtpldt0(u,v),slsdtgt0(xc)) ),
inference(res,[status(thm),theory(equality)],[13,63]),
[iquote('0:Res:13.0,63.0')] ).
cnf(430,plain,
( ~ aElement0(u)
| aSet0(slsdtgt0(u)) ),
inference(eqr,[status(thm),theory(equality)],[38]),
[iquote('0:EqR:38.1')] ).
cnf(800,plain,
( ~ aElement0(skf28(slsdtgt0(xc)))
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| aElementOf0(skf27(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(res,[status(thm),theory(equality)],[47,58]),
[iquote('0:Res:47.2,58.1')] ).
cnf(801,plain,
( ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| aElementOf0(skf27(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(ssi,[status(thm)],[800,430,3,4]),
[iquote('0:SSi:800.1,800.0,430.0,3.1,4.0,430.0,3.1')] ).
cnf(802,plain,
( ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc))
| aElementOf0(skf27(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(mrr,[status(thm)],[801,5]),
[iquote('0:MRR:801.1,5.0')] ).
cnf(1997,plain,
( ~ aElement0(skf28(slsdtgt0(xc)))
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(skf26(slsdtgt0(xc)),skf27(slsdtgt0(xc))),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc)) ),
inference(res,[status(thm),theory(equality)],[47,75]),
[iquote('0:Res:47.2,75.2')] ).
cnf(2000,plain,
( ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(skf26(slsdtgt0(xc)),skf27(slsdtgt0(xc))),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc)) ),
inference(ssi,[status(thm)],[1997,430,3,4]),
[iquote('0:SSi:1997.1,1997.0,430.0,3.1,4.0,430.0,3.1')] ).
cnf(2001,plain,
( ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(skf26(slsdtgt0(xc)),skf27(slsdtgt0(xc))),slsdtgt0(xc)) ),
inference(mrr,[status(thm)],[2000,5]),
[iquote('0:MRR:2000.2,5.0')] ).
cnf(13781,plain,
( ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(skf27(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(res,[status(thm),theory(equality)],[116,2001]),
[iquote('0:Res:116.2,2001.1')] ).
cnf(13783,plain,
( ~ aElementOf0(skf27(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(obv,[status(thm),theory(equality)],[13781]),
[iquote('0:Obv:13781.0')] ).
cnf(13784,plain,
~ aElementOf0(skf26(slsdtgt0(xc)),slsdtgt0(xc)),
inference(mrr,[status(thm)],[13783,802]),
[iquote('0:MRR:13783.0,802.1')] ).
cnf(13788,plain,
( ~ aSet0(slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc)) ),
inference(res,[status(thm),theory(equality)],[28,13784]),
[iquote('0:Res:28.2,13784.0')] ).
cnf(13793,plain,
aIdeal0(slsdtgt0(xc)),
inference(ssi,[status(thm)],[13788,430,3]),
[iquote('0:SSi:13788.0,430.0,3.1')] ).
cnf(13794,plain,
$false,
inference(mrr,[status(thm)],[13793,5]),
[iquote('0:MRR:13793.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : RNG106+1 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.10 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon May 30 11:44:27 EDT 2022
% 0.09/0.29 % CPUTime :
% 4.19/4.44
% 4.19/4.44 SPASS V 3.9
% 4.19/4.44 SPASS beiseite: Proof found.
% 4.19/4.44 % SZS status Theorem
% 4.19/4.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.19/4.44 SPASS derived 9319 clauses, backtracked 949 clauses, performed 4 splits and kept 3326 clauses.
% 4.19/4.44 SPASS allocated 108523 KBytes.
% 4.19/4.44 SPASS spent 0:00:03.61 on the problem.
% 4.19/4.44 0:00:00.03 for the input.
% 4.19/4.44 0:00:00.09 for the FLOTTER CNF translation.
% 4.19/4.44 0:00:00.15 for inferences.
% 4.19/4.44 0:00:00.04 for the backtracking.
% 4.19/4.44 0:00:03.23 for the reduction.
% 4.19/4.44
% 4.19/4.44
% 4.19/4.44 Here is a proof with depth 3, length 24 :
% 4.19/4.44 % SZS output start Refutation
% See solution above
% 4.19/4.44 Formulae used in the proof : m__1905 mDefIdeal m__ mDefPrIdeal
% 4.19/4.44
%------------------------------------------------------------------------------