TSTP Solution File: DAT105_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT105_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %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 : 300s
% DateTime : Sun May 5 05:06:03 EDT 2024
% Result : Theorem 0.17s 0.37s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 58 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 173 ( 46 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 207 ( 83 ~; 71 |; 43 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 252 ( 74 atm; 50 fun; 53 num; 75 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 119 ( 103 !; 16 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
nil: list ).
tff(func_def_1,type,
cons: ( $int * list ) > list ).
tff(func_def_2,type,
head: list > $int ).
tff(func_def_3,type,
tail: list > list ).
tff(func_def_10,type,
sK1: ( $int * list ) > $int ).
tff(func_def_11,type,
sK2: ( $int * list ) > list ).
tff(pred_def_1,type,
inRange: ( $int * list ) > $o ).
tff(pred_def_5,type,
sP0: ( $int * list ) > $o ).
tff(f491,plain,
$false,
inference(evaluation,[],[f484]) ).
tff(f484,plain,
~ $less($sum(1,0),2),
inference(resolution,[],[f471,f72]) ).
tff(f72,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f65,f10]) ).
tff(f10,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f65,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f19,f15]) ).
tff(f15,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f19,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f471,plain,
! [X0: $int] :
( ~ $less(X0,2)
| ~ $less(0,X0) ),
inference(evaluation,[],[f446]) ).
tff(f446,plain,
! [X0: $int] :
( ~ $less(X0,2)
| ~ $less(0,$sum(0,X0)) ),
inference(resolution,[],[f440,f15]) ).
tff(f440,plain,
! [X0: $int,X1: $int] :
( $less(X0,0)
| ~ $less(X1,2)
| ~ $less(X0,$sum(X0,X1)) ),
inference(evaluation,[],[f417]) ).
tff(f417,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,2)
| $less(X0,0)
| ~ $less(X0,$sum($uminus($uminus(X0)),X1)) ),
inference(superposition,[],[f342,f246]) ).
tff(f246,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f222]) ).
tff(f222,plain,
! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
inference(superposition,[],[f11,f14]) ).
tff(f14,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f11,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f342,plain,
! [X0: $int,X1: $int] :
( ~ $less($sum($uminus(X1),X0),2)
| $less(X1,0)
| ~ $less(X1,X0) ),
inference(superposition,[],[f330,f10]) ).
tff(f330,plain,
! [X0: $int,X1: $int] :
( ~ $less($sum(X1,$uminus(X0)),2)
| $less(X0,0)
| ~ $less(X0,X1) ),
inference(resolution,[],[f328,f49]) ).
tff(f49,plain,
! [X0: $int] : sP0(X0,nil),
inference(equality_resolution,[],[f44]) ).
tff(f44,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ( nil != X1 ) ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: $int,X1: list] :
( ( sP0(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) )
& ( nil != X1 ) ) )
& ( ( inRange(X0,sK2(X0,X1))
& $less(sK1(X0,X1),X0)
& ~ $less(sK1(X0,X1),0)
& ( cons(sK1(X0,X1),sK2(X0,X1)) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f31,f32]) ).
tff(f32,plain,
! [X0: $int,X1: list] :
( ? [X4: $int,X5: list] :
( inRange(X0,X5)
& $less(X4,X0)
& ~ $less(X4,0)
& ( cons(X4,X5) = X1 ) )
=> ( inRange(X0,sK2(X0,X1))
& $less(sK1(X0,X1),X0)
& ~ $less(sK1(X0,X1),0)
& ( cons(sK1(X0,X1),sK2(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
! [X0: $int,X1: list] :
( ( sP0(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) )
& ( nil != X1 ) ) )
& ( ? [X4: $int,X5: list] :
( inRange(X0,X5)
& $less(X4,X0)
& ~ $less(X4,0)
& ( cons(X4,X5) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f30]) ).
tff(f30,plain,
! [X0: $int,X1: list] :
( ( sP0(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) )
& ( nil != X1 ) ) )
& ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& $less(X2,X0)
& ~ $less(X2,0)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f29]) ).
tff(f29,plain,
! [X0: $int,X1: list] :
( ( sP0(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) )
& ( nil != X1 ) ) )
& ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& $less(X2,X0)
& ~ $less(X2,0)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f27]) ).
tff(f27,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& $less(X2,X0)
& ~ $less(X2,0)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f328,plain,
! [X2: list,X0: $int,X1: $int] :
( ~ sP0(X0,X2)
| ~ $less(X1,X0)
| $less(X1,0)
| ~ $less($sum(X0,$uminus(X1)),2) ),
inference(resolution,[],[f327,f47]) ).
tff(f47,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
inference(nnf_transformation,[],[f28]) ).
tff(f28,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f24,f27]) ).
tff(f24,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( inRange(X0,X3)
& $less(X2,X0)
& ~ $less(X2,0)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,plain,
! [X2: $int,X1: list] :
( inRange(X2,X1)
<=> ( ? [X0: $int,X3: list] :
( inRange(X2,X3)
& $less(X0,X2)
& ~ $less(X0,0)
& ( cons(X0,X3) = X1 ) )
| ( nil = X1 ) ) ),
inference(theory_normalization,[],[f5]) ).
tff(f5,axiom,
! [X2: $int,X1: list] :
( inRange(X2,X1)
<=> ( ? [X0: $int,X3: list] :
( inRange(X2,X3)
& $less(X0,X2)
& $lesseq(0,X0)
& ( cons(X0,X3) = X1 ) )
| ( nil = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f327,plain,
! [X2: $int,X0: $int,X1: list] :
( ~ inRange(X0,X1)
| ~ $less($sum(X0,$uminus(X2)),2)
| ~ $less(X2,X0)
| $less(X2,0) ),
inference(forward_demodulation,[],[f326,f39]) ).
tff(f39,plain,
! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
tff(f326,plain,
! [X2: $int,X0: $int,X1: list] :
( ~ inRange(X0,X1)
| ~ $less(X2,X0)
| $less(X2,0)
| ~ $less($sum(X0,$uminus(head(cons(X2,X1)))),2) ),
inference(subsumption_resolution,[],[f321,f37]) ).
tff(f37,plain,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(f321,plain,
! [X2: $int,X0: $int,X1: list] :
( ~ inRange(X0,X1)
| ~ $less(X2,X0)
| $less(X2,0)
| ~ $less($sum(X0,$uminus(head(cons(X2,X1)))),2)
| ( nil = cons(X2,X1) ) ),
inference(resolution,[],[f48,f51]) ).
tff(f51,plain,
! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| ~ $less($sum(X0,$uminus(head(X1))),2)
| ( nil = X1 ) ),
inference(resolution,[],[f47,f35]) ).
tff(f35,plain,
! [X0: list,X1: $int] :
( ~ inRange(X1,X0)
| ~ $less($sum(X1,$uminus(head(X0))),2)
| ( nil = X0 ) ),
inference(cnf_transformation,[],[f26]) ).
tff(f26,plain,
! [X0: list,X1: $int] :
( ~ $less($sum(X1,$uminus(head(X0))),2)
| ~ inRange(X1,X0)
| ( nil = X0 ) ),
inference(flattening,[],[f25]) ).
tff(f25,plain,
! [X0: list,X1: $int] :
( ~ $less($sum(X1,$uminus(head(X0))),2)
| ~ inRange(X1,X0)
| ( nil = X0 ) ),
inference(ennf_transformation,[],[f22]) ).
tff(f22,plain,
! [X0: list,X1: $int] :
( ( inRange(X1,X0)
& ( nil != X0 ) )
=> ~ $less($sum(X1,$uminus(head(X0))),2) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
! [X1: list,X2: $int] :
( ( inRange(X2,X1)
& ( nil != X1 ) )
=> ~ $less($sum(X2,$uminus(head(X1))),2) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ~ ! [X1: list,X2: $int] :
( ( inRange(X2,X1)
& ( nil != X1 ) )
=> $greatereq($difference(X2,head(X1)),2) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
~ ! [X1: list,X2: $int] :
( ( inRange(X2,X1)
& ( nil != X1 ) )
=> $greatereq($difference(X2,head(X1)),2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f48,plain,
! [X2: $int,X3: list,X0: $int] :
( sP0(X0,cons(X2,X3))
| ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0) ),
inference(equality_resolution,[],[f45]) ).
tff(f45,plain,
! [X2: $int,X3: list,X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X3)
| ~ $less(X2,X0)
| $less(X2,0)
| ( cons(X2,X3) != X1 ) ),
inference(cnf_transformation,[],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : DAT105_1 : TPTP v8.1.2. Released v6.1.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 12:58:05 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (22291)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (22294)WARNING: value z3 for option sas not known
% 0.17/0.34 % (22296)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.34 % (22297)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.34 % (22292)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.34 % (22294)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.34 % (22295)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.34 % (22298)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.34 % (22293)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.34 % (22292)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.17/0.34 % (22292)Terminated due to inappropriate strategy.
% 0.17/0.34 % (22292)------------------------------
% 0.17/0.34 % (22292)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.34 % (22292)Termination reason: Inappropriate
% 0.17/0.34
% 0.17/0.34 % (22292)Memory used [KB]: 730
% 0.17/0.34 % (22292)Time elapsed: 0.002 s
% 0.17/0.34 % (22292)Instructions burned: 2 (million)
% 0.17/0.34 % (22295)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.17/0.34 % (22295)Terminated due to inappropriate strategy.
% 0.17/0.34 % (22295)------------------------------
% 0.17/0.34 % (22295)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.34 % (22292)------------------------------
% 0.17/0.34 % (22292)------------------------------
% 0.17/0.34 % (22295)Termination reason: Inappropriate
% 0.17/0.34
% 0.17/0.34 % (22295)Memory used [KB]: 730
% 0.17/0.34 % (22295)Time elapsed: 0.002 s
% 0.17/0.34 % (22295)Instructions burned: 2 (million)
% 0.17/0.34 % (22293)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.17/0.34 % (22293)Terminated due to inappropriate strategy.
% 0.17/0.34 % (22293)------------------------------
% 0.17/0.34 % (22293)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.34 % (22293)Termination reason: Inappropriate
% 0.17/0.34
% 0.17/0.34 % (22293)Memory used [KB]: 730
% 0.17/0.34 % (22293)Time elapsed: 0.002 s
% 0.17/0.34 % (22293)Instructions burned: 2 (million)
% 0.17/0.34 % (22295)------------------------------
% 0.17/0.34 % (22295)------------------------------
% 0.17/0.34 % (22293)------------------------------
% 0.17/0.34 % (22293)------------------------------
% 0.17/0.36 % (22299)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.17/0.36 % (22301)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.17/0.36 % (22300)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.17/0.36 % (22299)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.17/0.36 % (22299)Terminated due to inappropriate strategy.
% 0.17/0.36 % (22299)------------------------------
% 0.17/0.36 % (22299)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.36 % (22299)Termination reason: Inappropriate
% 0.17/0.36
% 0.17/0.36 % (22299)Memory used [KB]: 730
% 0.17/0.36 % (22299)Time elapsed: 0.002 s
% 0.17/0.36 % (22299)Instructions burned: 2 (million)
% 0.17/0.36 % (22299)------------------------------
% 0.17/0.36 % (22299)------------------------------
% 0.17/0.37 % (22301)First to succeed.
% 0.17/0.37 % (22302)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.17/0.37 % (22301)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22291"
% 0.17/0.37 % (22301)Refutation found. Thanks to Tanya!
% 0.17/0.37 % SZS status Theorem for theBenchmark
% 0.17/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.37 % (22301)------------------------------
% 0.17/0.37 % (22301)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.37 % (22301)Termination reason: Refutation
% 0.17/0.37
% 0.17/0.37 % (22301)Memory used [KB]: 942
% 0.17/0.37 % (22301)Time elapsed: 0.016 s
% 0.17/0.37 % (22301)Instructions burned: 26 (million)
% 0.17/0.37 % (22291)Success in time 0.045 s
%------------------------------------------------------------------------------