TSTP Solution File: DAT104_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT104_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 : n026.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 1.62s 0.60s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 52 ( 17 unt; 9 typ; 0 def)
% Number of atoms : 140 ( 33 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 149 ( 52 ~; 48 |; 39 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 156 ( 41 atm; 18 fun; 47 num; 50 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 74 !; 16 ?; 90 :)
% 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_9,type,
sK1: ( $int * list ) > $int ).
tff(func_def_10,type,
sK2: ( $int * list ) > list ).
tff(pred_def_1,type,
inRange: ( $int * list ) > $o ).
tff(pred_def_4,type,
sP0: ( $int * list ) > $o ).
tff(f15940,plain,
$false,
inference(subsumption_resolution,[],[f15932,f15933]) ).
tff(f15933,plain,
~ $less(sK1(0,cons(0,nil)),0),
inference(unit_resulting_resolution,[],[f36,f15386,f40]) ).
tff(f40,plain,
! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| ( nil = X1 )
| ~ $less(sK1(X0,X1),0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,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])],[f30,f31]) ).
tff(f31,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(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 ) ) )
& ( ? [X4: $int,X5: list] :
( inRange(X0,X5)
& $less(X4,X0)
& ~ $less(X4,0)
& ( cons(X4,X5) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[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(flattening,[],[f28]) ).
tff(f28,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,[],[f26]) ).
tff(f26,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(f15386,plain,
sP0(0,cons(0,nil)),
inference(unit_resulting_resolution,[],[f15384,f45]) ).
tff(f45,plain,
! [X0: $int,X1: list] :
( ~ inRange(X0,X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
inference(nnf_transformation,[],[f27]) ).
tff(f27,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f24,f26]) ).
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)
& $lesseq(0,X0)
& ( cons(X0,X3) = X1 ) )
| ( nil = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange) ).
tff(f15384,plain,
inRange(0,cons(0,nil)),
inference(evaluation,[],[f15378]) ).
tff(f15378,plain,
inRange($sum(1,-1),cons(0,nil)),
inference(unit_resulting_resolution,[],[f15333,f49]) ).
tff(f49,plain,
! [X0: $int,X1: list] :
( ~ inRange(X0,X1)
| inRange($sum(X0,-1),X1) ),
inference(evaluation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: list] :
( inRange($sum(X0,$uminus(1)),X1)
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: $int,X1: list] :
( inRange($sum(X0,$uminus(1)),X1)
| ~ inRange(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
tff(f22,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
=> inRange($sum(X0,$uminus(1)),X1) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
! [X2: $int,X1: list] :
( inRange(X2,X1)
=> inRange($sum(X2,$uminus(1)),X1) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ~ ! [X2: $int,X1: list] :
( inRange(X2,X1)
=> inRange($difference(X2,1),X1) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
~ ! [X2: $int,X1: list] :
( inRange(X2,X1)
=> inRange($difference(X2,1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f15333,plain,
inRange(1,cons(0,nil)),
inference(unit_resulting_resolution,[],[f13581,f46]) ).
tff(f46,plain,
! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| inRange(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tff(f13581,plain,
sP0(1,cons(0,nil)),
inference(evaluation,[],[f11817]) ).
tff(f11817,plain,
sP0($sum(1,0),cons(0,nil)),
inference(unit_resulting_resolution,[],[f51,f75,f15,f47]) ).
tff(f47,plain,
! [X2: $int,X3: list,X0: $int] :
( ~ inRange(X0,X3)
| sP0(X0,cons(X2,X3))
| ~ $less(X2,X0)
| $less(X2,0) ),
inference(equality_resolution,[],[f44]) ).
tff(f44,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,[],[f32]) ).
tff(f15,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f75,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f69,f10]) ).
tff(f10,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f69,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(unit_resulting_resolution,[],[f15,f19]) ).
tff(f19,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_147,[]) ).
tff(f51,plain,
! [X0: $int] : inRange(X0,nil),
inference(unit_resulting_resolution,[],[f48,f46]) ).
tff(f48,plain,
! [X0: $int] : sP0(X0,nil),
inference(equality_resolution,[],[f43]) ).
tff(f43,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ( nil != X1 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f36,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/sandbox2/benchmark/theBenchmark.p',l4) ).
tff(f15932,plain,
$less(sK1(0,cons(0,nil)),0),
inference(unit_resulting_resolution,[],[f36,f15386,f41]) ).
tff(f41,plain,
! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| ( nil = X1 )
| $less(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : DAT104_1 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 13:17:21 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (32573)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (32574)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (32574)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38 % (32574)Terminated due to inappropriate strategy.
% 0.14/0.38 % (32574)------------------------------
% 0.14/0.38 % (32574)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (32574)Termination reason: Inappropriate
% 0.14/0.38
% 0.14/0.38 % (32574)Memory used [KB]: 729
% 0.14/0.38 % (32574)Time elapsed: 0.002 s
% 0.14/0.38 % (32574)Instructions burned: 2 (million)
% 0.14/0.39 % (32574)------------------------------
% 0.14/0.39 % (32574)------------------------------
% 0.14/0.39 % (32577)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (32580)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)
% 0.14/0.39 % (32577)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39 % (32577)Terminated due to inappropriate strategy.
% 0.14/0.39 % (32577)------------------------------
% 0.14/0.39 % (32577)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (32577)Termination reason: Inappropriate
% 0.14/0.39
% 0.14/0.39 % (32577)Memory used [KB]: 729
% 0.14/0.39 % (32577)Time elapsed: 0.002 s
% 0.14/0.39 % (32577)Instructions burned: 2 (million)
% 0.14/0.39 % (32577)------------------------------
% 0.14/0.39 % (32577)------------------------------
% 0.14/0.39 % (32579)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)
% 0.14/0.39 % (32576)WARNING: value z3 for option sas not known
% 0.14/0.39 % (32575)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (32576)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)
% 0.14/0.39 % (32578)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)
% 0.14/0.39 % (32575)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39 % (32575)Terminated due to inappropriate strategy.
% 0.14/0.39 % (32575)------------------------------
% 0.14/0.39 % (32575)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (32575)Termination reason: Inappropriate
% 0.14/0.39
% 0.14/0.39 % (32575)Memory used [KB]: 730
% 0.14/0.39 % (32575)Time elapsed: 0.003 s
% 0.14/0.39 % (32575)Instructions burned: 2 (million)
% 0.14/0.39 % (32575)------------------------------
% 0.14/0.39 % (32575)------------------------------
% 0.14/0.40 % (32581)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40 % (32581)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40 % (32581)Terminated due to inappropriate strategy.
% 0.14/0.40 % (32581)------------------------------
% 0.14/0.40 % (32581)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (32581)Termination reason: Inappropriate
% 0.14/0.40
% 0.14/0.40 % (32581)Memory used [KB]: 729
% 0.14/0.40 % (32581)Time elapsed: 0.003 s
% 0.14/0.40 % (32581)Instructions burned: 2 (million)
% 0.14/0.40 % (32581)------------------------------
% 0.14/0.40 % (32581)------------------------------
% 0.14/0.41 % (32582)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)
% 0.14/0.41 % (32583)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)
% 0.14/0.42 % (32584)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)
% 1.62/0.60 % (32582)First to succeed.
% 1.62/0.60 % (32582)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-32573"
% 1.62/0.60 % (32582)Refutation found. Thanks to Tanya!
% 1.62/0.60 % SZS status Theorem for theBenchmark
% 1.62/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.62/0.60 % (32582)------------------------------
% 1.62/0.60 % (32582)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.62/0.60 % (32582)Termination reason: Refutation
% 1.62/0.60
% 1.62/0.60 % (32582)Memory used [KB]: 2962
% 1.62/0.60 % (32582)Time elapsed: 0.195 s
% 1.62/0.60 % (32582)Instructions burned: 440 (million)
% 1.62/0.60 % (32573)Success in time 0.231 s
%------------------------------------------------------------------------------