TSTP Solution File: DAT088_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT088_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 : n003.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 : Tue Apr 30 11:04:02 EDT 2024
% Result : Theorem 0.22s 0.38s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 57 ( 13 unt; 18 typ; 0 def)
% Number of atoms : 115 ( 63 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 116 ( 40 ~; 35 |; 28 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 83 ( 9 atm; 0 fun; 12 num; 62 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 29 ( 16 >; 13 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 121 ( 93 !; 28 ?; 121 :)
% 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_5,type,
length: list > $int ).
tff(func_def_8,type,
count: ( $int * list ) > $int ).
tff(func_def_9,type,
append: ( list * list ) > list ).
tff(func_def_11,type,
sK2: ( $int * list ) > $int ).
tff(func_def_12,type,
sK3: ( $int * list ) > list ).
tff(func_def_13,type,
sK4: ( $int * list ) > $int ).
tff(func_def_14,type,
sK5: ( $int * list ) > list ).
tff(func_def_15,type,
sK6: ( $int * list ) > $int ).
tff(func_def_16,type,
sK7: ( $int * list ) > list ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,type,
inRange: ( $int * list ) > $o ).
tff(pred_def_6,type,
sP0: ( $int * list ) > $o ).
tff(pred_def_7,type,
sP1: ( $int * list ) > $o ).
tff(f193,plain,
$false,
inference(evaluation,[],[f190]) ).
tff(f190,plain,
$less(0,0),
inference(superposition,[],[f183,f65]) ).
tff(f65,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: $int] : ( 0 = count(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
tff(f183,plain,
! [X0: $int,X1: list] : $less(0,count(X0,X1)),
inference(superposition,[],[f142,f181]) ).
tff(f181,plain,
! [X2: $int,X0: $int,X1: list] : ( count(X2,cons(X0,X1)) = count(X2,X1) ),
inference(subsumption_resolution,[],[f179,f68]) ).
tff(f68,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(f179,plain,
! [X2: $int,X0: $int,X1: list] :
( ( count(X2,cons(X0,X1)) = count(X2,X1) )
| ( cons(X0,X1) = nil ) ),
inference(superposition,[],[f63,f70]) ).
tff(f70,plain,
! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
tff(f63,plain,
! [X0: $int,X1: list] :
( ( count(X0,X1) = count(X0,tail(X1)) )
| ( nil = X1 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: $int,X1: list] :
( ( count(X0,X1) = count(X0,tail(X1)) )
| ( nil = X1 ) ),
inference(ennf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: list] :
( ( nil != X1 )
=> ( count(X0,X1) = count(X0,tail(X1)) ) ),
inference(flattening,[],[f31]) ).
tff(f31,plain,
~ ~ ! [X0: $int,X1: list] :
( ( nil != X1 )
=> ( count(X0,X1) = count(X0,tail(X1)) ) ),
inference(rectify,[],[f16]) ).
tff(f16,negated_conjecture,
~ ~ ! [X5: $int,X1: list] :
( ( nil != X1 )
=> ( count(X5,X1) = count(X5,tail(X1)) ) ),
inference(negated_conjecture,[],[f15]) ).
tff(f15,conjecture,
~ ! [X5: $int,X1: list] :
( ( nil != X1 )
=> ( count(X5,X1) = count(X5,tail(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f142,plain,
! [X0: $int,X1: list] : $less(0,count(X0,cons(X0,X1))),
inference(resolution,[],[f80,f102]) ).
tff(f102,plain,
! [X0: $int,X1: list] : in(X0,cons(X0,X1)),
inference(resolution,[],[f89,f97]) ).
tff(f97,plain,
! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
inference(equality_resolution,[],[f96]) ).
tff(f96,plain,
! [X1: list,X4: $int,X5: list] :
( sP1(X4,X1)
| ( cons(X4,X5) != X1 ) ),
inference(equality_resolution,[],[f86]) ).
tff(f86,plain,
! [X0: $int,X1: list,X4: $int,X5: list] :
( sP1(X0,X1)
| ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ),
inference(cnf_transformation,[],[f61]) ).
tff(f61,plain,
! [X0: $int,X1: list] :
( ( sP1(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) )
& ! [X4: $int,X5: list] :
( ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ) ) )
& ( ( in(X0,sK5(X0,X1))
& ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) )
| ( ( sK6(X0,X1) = X0 )
& ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f58,f60,f59]) ).
tff(f59,plain,
! [X0: $int,X1: list] :
( ? [X6: $int,X7: list] :
( in(X0,X7)
& ( cons(X6,X7) = X1 ) )
=> ( in(X0,sK5(X0,X1))
& ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f60,plain,
! [X0: $int,X1: list] :
( ? [X8: $int,X9: list] :
( ( X0 = X8 )
& ( cons(X8,X9) = X1 ) )
=> ( ( sK6(X0,X1) = X0 )
& ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f58,plain,
! [X0: $int,X1: list] :
( ( sP1(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) )
& ! [X4: $int,X5: list] :
( ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ) ) )
& ( ? [X6: $int,X7: list] :
( in(X0,X7)
& ( cons(X6,X7) = X1 ) )
| ? [X8: $int,X9: list] :
( ( X0 = X8 )
& ( cons(X8,X9) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f57]) ).
tff(f57,plain,
! [X0: $int,X1: list] :
( ( sP1(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) )
& ! [X4: $int,X5: list] :
( ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ) ) )
& ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: $int,X5: list] :
( ( X0 = X4 )
& ( cons(X4,X5) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(flattening,[],[f56]) ).
tff(f56,plain,
! [X0: $int,X1: list] :
( ( sP1(X0,X1)
| ( ! [X2: $int,X3: list] :
( ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) )
& ! [X4: $int,X5: list] :
( ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ) ) )
& ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: $int,X5: list] :
( ( X0 = X4 )
& ( cons(X4,X5) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0: $int,X1: list] :
( sP1(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: $int,X5: list] :
( ( X0 = X4 )
& ( cons(X4,X5) = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f89,plain,
! [X0: $int,X1: list] :
( ~ sP1(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tff(f62,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f38,f47]) ).
tff(f38,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ? [X4: $int,X5: list] :
( ( X0 = X4 )
& ( cons(X4,X5) = X1 ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X2: $int,X1: list] :
( in(X2,X1)
<=> ( ? [X3: $int,X4: list] :
( in(X2,X4)
& ( cons(X3,X4) = X1 ) )
| ? [X3: $int,X4: list] :
( ( X2 = X3 )
& ( cons(X3,X4) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_conv) ).
tff(f80,plain,
! [X0: $int,X1: list] :
( ~ in(X0,X1)
| $less(0,count(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
tff(f55,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ $less(0,count(X0,X1)) )
& ( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> $less(0,count(X0,X1)) ),
inference(rectify,[],[f18]) ).
tff(f18,plain,
! [X5: $int,X1: list] :
( in(X5,X1)
<=> $less(0,count(X5,X1)) ),
inference(theory_normalization,[],[f14]) ).
tff(f14,axiom,
! [X5: $int,X1: list] :
( in(X5,X1)
<=> $greater(count(X5,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_8) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT088_1 : TPTP v8.1.2. Released v6.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n003.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 : 300
% 0.15/0.35 % DateTime : Mon Apr 29 22:22:18 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (12525)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (12528)WARNING: value z3 for option sas not known
% 0.15/0.38 % (12529)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (12526)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (12527)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (12528)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)
% 0.15/0.38 % (12530)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)
% 0.15/0.38 % (12531)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)
% 0.15/0.38 % (12532)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)
% 0.15/0.38 % (12529)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (12527)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (12526)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38 % (12527)Terminated due to inappropriate strategy.
% 0.15/0.38 % (12527)------------------------------
% 0.15/0.38 % (12527)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (12527)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (12526)Terminated due to inappropriate strategy.
% 0.15/0.38 % (12526)------------------------------
% 0.15/0.38 % (12526)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (12527)Memory used [KB]: 803
% 0.15/0.38 % (12526)Termination reason: Inappropriate
% 0.15/0.38 % (12527)Time elapsed: 0.003 s
% 0.15/0.38
% 0.15/0.38 % (12527)Instructions burned: 3 (million)
% 0.15/0.38 % (12526)Memory used [KB]: 803
% 0.15/0.38 % (12527)------------------------------
% 0.15/0.38 % (12527)------------------------------
% 0.15/0.38 % (12526)Time elapsed: 0.003 s
% 0.15/0.38 % (12526)Instructions burned: 3 (million)
% 0.15/0.38 % (12526)------------------------------
% 0.15/0.38 % (12526)------------------------------
% 0.15/0.38 % (12529)Terminated due to inappropriate strategy.
% 0.15/0.38 % (12529)------------------------------
% 0.15/0.38 % (12529)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (12529)Termination reason: Inappropriate
% 0.15/0.38
% 0.15/0.38 % (12529)Memory used [KB]: 803
% 0.15/0.38 % (12529)Time elapsed: 0.003 s
% 0.15/0.38 % (12529)Instructions burned: 3 (million)
% 0.15/0.38 % (12529)------------------------------
% 0.15/0.38 % (12529)------------------------------
% 0.15/0.38 % (12528)First to succeed.
% 0.22/0.38 % (12528)Refutation found. Thanks to Tanya!
% 0.22/0.38 % SZS status Theorem for theBenchmark
% 0.22/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38 % (12528)------------------------------
% 0.22/0.38 % (12528)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.38 % (12528)Termination reason: Refutation
% 0.22/0.38
% 0.22/0.38 % (12528)Memory used [KB]: 878
% 0.22/0.38 % (12528)Time elapsed: 0.009 s
% 0.22/0.38 % (12528)Instructions burned: 10 (million)
% 0.22/0.38 % (12528)------------------------------
% 0.22/0.38 % (12528)------------------------------
% 0.22/0.38 % (12525)Success in time 0.014 s
%------------------------------------------------------------------------------