TSTP Solution File: RNG111+4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG111+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 20:41:30 EDT 2022
% Result : Theorem 0.48s 0.68s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 48 ( 25 unt; 2 nHn; 48 RR)
% Number of literals : 80 ( 0 equ; 42 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
aSet0(xI),
file('RNG111+4.p',unknown),
[] ).
cnf(14,axiom,
aElementOf0(skc18,xI),
file('RNG111+4.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(skc15,xI),
file('RNG111+4.p',unknown),
[] ).
cnf(26,axiom,
aElementOf0(skf27(u),xI),
file('RNG111+4.p',unknown),
[] ).
cnf(31,axiom,
~ equal(sz00,skc15),
file('RNG111+4.p',unknown),
[] ).
cnf(59,axiom,
( ~ aElementOf0(u,xI)
| skP5(u) ),
file('RNG111+4.p',unknown),
[] ).
cnf(67,axiom,
( ~ skP5(u)
| skP6(u)
| equal(u,sz00) ),
file('RNG111+4.p',unknown),
[] ).
cnf(78,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG111+4.p',unknown),
[] ).
cnf(95,axiom,
( ~ skP5(u)
| ~ equal(skf27(u),sz00)
| equal(u,sz00) ),
file('RNG111+4.p',unknown),
[] ).
cnf(104,axiom,
( ~ skP5(u)
| equal(u,sz00)
| iLess0(sbrdtbr0(skf27(u)),sbrdtbr0(u)) ),
file('RNG111+4.p',unknown),
[] ).
cnf(107,axiom,
( ~ skP6(u)
| ~ equal(sz00,skc18)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc15)) ),
file('RNG111+4.p',unknown),
[] ).
cnf(133,axiom,
( ~ skP6(u)
| ~ skP6(v)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc15))
| ~ iLess0(sbrdtbr0(v),sbrdtbr0(skc18)) ),
file('RNG111+4.p',unknown),
[] ).
cnf(170,plain,
skP5(skc15),
inference(res,[status(thm),theory(equality)],[15,59]),
[iquote('0:Res:15.0,59.0')] ).
cnf(178,plain,
( ~ aSet0(xI)
| aElement0(skc15) ),
inference(res,[status(thm),theory(equality)],[15,78]),
[iquote('0:Res:15.0,78.1')] ).
cnf(187,plain,
skP5(skc18),
inference(res,[status(thm),theory(equality)],[14,59]),
[iquote('0:Res:14.0,59.0')] ).
cnf(195,plain,
( ~ aSet0(xI)
| aElement0(skc18) ),
inference(res,[status(thm),theory(equality)],[14,78]),
[iquote('0:Res:14.0,78.1')] ).
cnf(205,plain,
( ~ skP5(skc15)
| iLess0(sbrdtbr0(skf27(skc15)),sbrdtbr0(skc15)) ),
inference(res,[status(thm),theory(equality)],[104,31]),
[iquote('0:Res:104.2,31.0')] ).
cnf(206,plain,
( ~ skP5(skc15)
| ~ equal(skf27(skc15),sz00) ),
inference(res,[status(thm),theory(equality)],[95,31]),
[iquote('0:Res:95.2,31.0')] ).
cnf(208,plain,
( ~ skP5(skc15)
| skP6(skc15) ),
inference(res,[status(thm),theory(equality)],[67,31]),
[iquote('0:Res:67.1,31.0')] ).
cnf(279,plain,
skP5(skf27(u)),
inference(res,[status(thm),theory(equality)],[26,59]),
[iquote('0:Res:26.0,59.0')] ).
cnf(287,plain,
( ~ aSet0(xI)
| aElement0(skf27(u)) ),
inference(res,[status(thm),theory(equality)],[26,78]),
[iquote('0:Res:26.0,78.1')] ).
cnf(361,plain,
aElement0(skc15),
inference(mrr,[status(thm)],[178,8]),
[iquote('0:MRR:178.0,8.0')] ).
cnf(362,plain,
aElement0(skc18),
inference(mrr,[status(thm)],[195,8]),
[iquote('0:MRR:195.0,8.0')] ).
cnf(363,plain,
skP6(skc15),
inference(mrr,[status(thm)],[208,170]),
[iquote('0:MRR:208.0,170.0')] ).
cnf(366,plain,
aElement0(skf27(u)),
inference(mrr,[status(thm)],[287,8]),
[iquote('0:MRR:287.0,8.0')] ).
cnf(367,plain,
~ equal(skf27(skc15),sz00),
inference(mrr,[status(thm)],[206,170]),
[iquote('0:MRR:206.0,170.0')] ).
cnf(369,plain,
iLess0(sbrdtbr0(skf27(skc15)),sbrdtbr0(skc15)),
inference(mrr,[status(thm)],[205,170]),
[iquote('0:MRR:205.0,170.0')] ).
cnf(403,plain,
( ~ skP6(u)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc15)) ),
inference(spt,[spt(split,[position(s1)])],[133]),
[iquote('1:Spt:133.0,133.2')] ).
cnf(420,plain,
~ skP6(skf27(skc15)),
inference(res,[status(thm),theory(equality)],[369,403]),
[iquote('1:Res:369.0,403.1')] ).
cnf(456,plain,
( ~ skP5(skf27(skc15))
| equal(skf27(skc15),sz00) ),
inference(sor,[status(thm)],[420,67]),
[iquote('1:SoR:420.0,67.1')] ).
cnf(457,plain,
equal(skf27(skc15),sz00),
inference(ssi,[status(thm)],[456,279,363,170,361,366]),
[iquote('1:SSi:456.0,279.0,363.0,170.0,361.0,366.0,363.0,170.0,361.0')] ).
cnf(458,plain,
$false,
inference(mrr,[status(thm)],[457,367]),
[iquote('1:MRR:457.0,367.0')] ).
cnf(459,plain,
( ~ skP6(u)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc18)) ),
inference(spt,[spt(split,[position(s2)])],[133]),
[iquote('1:Spt:458.0,133.1,133.3')] ).
cnf(460,plain,
( ~ skP6(u)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(skc15)) ),
inference(spt,[spt(split,[position(s2s1)])],[107]),
[iquote('2:Spt:107.0,107.2')] ).
cnf(461,plain,
~ skP6(skf27(skc15)),
inference(res,[status(thm),theory(equality)],[369,460]),
[iquote('2:Res:369.0,460.1')] ).
cnf(462,plain,
( ~ skP5(skf27(skc15))
| equal(skf27(skc15),sz00) ),
inference(sor,[status(thm)],[461,67]),
[iquote('2:SoR:461.0,67.1')] ).
cnf(463,plain,
equal(skf27(skc15),sz00),
inference(ssi,[status(thm)],[462,279,363,170,361,366]),
[iquote('2:SSi:462.0,279.0,363.0,170.0,361.0,366.0,363.0,170.0,361.0')] ).
cnf(464,plain,
$false,
inference(mrr,[status(thm)],[463,367]),
[iquote('2:MRR:463.0,367.0')] ).
cnf(465,plain,
~ equal(sz00,skc18),
inference(spt,[spt(split,[position(s2s2)])],[107]),
[iquote('2:Spt:464.0,107.1')] ).
cnf(738,plain,
( ~ skP5(skc18)
| ~ skP6(skf27(skc18))
| equal(sz00,skc18) ),
inference(res,[status(thm),theory(equality)],[104,459]),
[iquote('1:Res:104.2,459.1')] ).
cnf(739,plain,
( ~ skP6(skf27(skc18))
| equal(sz00,skc18) ),
inference(ssi,[status(thm)],[738,187,362]),
[iquote('1:SSi:738.0,187.0,362.0')] ).
cnf(740,plain,
~ skP6(skf27(skc18)),
inference(mrr,[status(thm)],[739,465]),
[iquote('2:MRR:739.1,465.0')] ).
cnf(741,plain,
( ~ skP5(skf27(skc18))
| equal(skf27(skc18),sz00) ),
inference(sor,[status(thm)],[740,67]),
[iquote('2:SoR:740.0,67.1')] ).
cnf(742,plain,
equal(skf27(skc18),sz00),
inference(ssi,[status(thm)],[741,279,187,362,366]),
[iquote('2:SSi:741.0,279.0,187.0,362.0,366.0,187.0,362.0')] ).
cnf(748,plain,
( ~ skP5(skc18)
| ~ equal(sz00,sz00)
| equal(sz00,skc18) ),
inference(spl,[status(thm),theory(equality)],[742,95]),
[iquote('2:SpL:742.0,95.1')] ).
cnf(749,plain,
( ~ skP5(skc18)
| equal(sz00,skc18) ),
inference(obv,[status(thm),theory(equality)],[748]),
[iquote('2:Obv:748.1')] ).
cnf(750,plain,
equal(sz00,skc18),
inference(ssi,[status(thm)],[749,187,362]),
[iquote('2:SSi:749.0,187.0,362.0')] ).
cnf(751,plain,
$false,
inference(mrr,[status(thm)],[750,465]),
[iquote('2:MRR:750.0,465.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG111+4 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon May 30 10:02:36 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.48/0.68
% 0.48/0.68 SPASS V 3.9
% 0.48/0.68 SPASS beiseite: Proof found.
% 0.48/0.68 % SZS status Theorem
% 0.48/0.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.68 SPASS derived 459 clauses, backtracked 6 clauses, performed 3 splits and kept 405 clauses.
% 0.48/0.68 SPASS allocated 100316 KBytes.
% 0.48/0.68 SPASS spent 0:00:00.32 on the problem.
% 0.48/0.68 0:00:00.04 for the input.
% 0.48/0.68 0:00:00.20 for the FLOTTER CNF translation.
% 0.48/0.68 0:00:00.01 for inferences.
% 0.48/0.68 0:00:00.00 for the backtracking.
% 0.48/0.68 0:00:00.02 for the reduction.
% 0.48/0.68
% 0.48/0.68
% 0.48/0.68 Here is a proof with depth 4, length 48 :
% 0.48/0.68 % SZS output start Refutation
% See solution above
% 0.48/0.69 Formulae used in the proof : m__2174 m__2203 m__2228 m__ mEOfElem
% 0.48/0.69
%------------------------------------------------------------------------------