TSTP Solution File: DAT087_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT087_1 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 : Mon May 20 19:51:23 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 50 ( 11 unt; 18 typ; 0 def)
% Number of atoms : 103 ( 49 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 109 ( 38 ~; 34 |; 28 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 82 ( 8 atm; 0 fun; 20 num; 54 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 : 15 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 76 !; 28 ?; 104 :)
% 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(f151,plain,
$false,
inference(resolution,[],[f148,f96]) ).
tff(f96,plain,
! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
inference(equality_resolution,[],[f95]) ).
tff(f95,plain,
! [X1: list,X4: $int,X5: list] :
( sP1(X4,X1)
| ( cons(X4,X5) != X1 ) ),
inference(equality_resolution,[],[f85]) ).
tff(f85,plain,
! [X0: $int,X1: list,X4: $int,X5: list] :
( sP1(X0,X1)
| ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ),
inference(cnf_transformation,[],[f60]) ).
tff(f60,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])],[f57,f59,f58]) ).
tff(f58,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(f59,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(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 ) ) ) )
& ( ? [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,[],[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(flattening,[],[f55]) ).
tff(f55,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,[],[f46]) ).
tff(f46,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(f148,plain,
! [X0: $int] : ~ sP1(X0,cons(1,nil)),
inference(resolution,[],[f146,f88]) ).
tff(f88,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tff(f61,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f38,f46]) ).
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(f146,plain,
! [X0: $int] : ~ in(X0,cons(1,nil)),
inference(evaluation,[],[f144]) ).
tff(f144,plain,
! [X0: $int] :
( $less(0,0)
| ~ in(X0,cons(1,nil)) ),
inference(superposition,[],[f138,f64]) ).
tff(f64,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(f138,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,cons(1,X1)) ),
inference(superposition,[],[f79,f62]) ).
tff(f62,plain,
! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
inference(flattening,[],[f31]) ).
tff(f31,plain,
~ ~ ! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
inference(rectify,[],[f16]) ).
tff(f16,negated_conjecture,
~ ~ ! [X5: $int,X1: list] : ( count(X5,X1) = count(X5,cons(1,X1)) ),
inference(negated_conjecture,[],[f15]) ).
tff(f15,conjecture,
~ ! [X5: $int,X1: list] : ( count(X5,X1) = count(X5,cons(1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f79,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,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
% 0.08/0.13 % Problem : DAT087_1 : TPTP v8.2.0. Released v6.1.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n012.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 23:05:38 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (30893)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (30896)WARNING: value z3 for option sas not known
% 0.15/0.39 % (30894)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (30895)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (30897)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (30896)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)
% 0.15/0.39 % (30899)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)
% 0.15/0.39 % (30898)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)
% 0.15/0.39 % (30900)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)
% 0.15/0.39 % (30895)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39 % (30897)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39 % (30894)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39 % (30895)Terminated due to inappropriate strategy.
% 0.15/0.39 % (30895)------------------------------
% 0.15/0.39 % (30895)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (30897)Terminated due to inappropriate strategy.
% 0.15/0.39 % (30897)------------------------------
% 0.15/0.39 % (30897)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (30894)Terminated due to inappropriate strategy.
% 0.15/0.39 % (30894)------------------------------
% 0.15/0.39 % (30894)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (30895)Termination reason: Inappropriate
% 0.15/0.39 % (30897)Termination reason: Inappropriate
% 0.15/0.39
% 0.15/0.39 % (30894)Termination reason: Inappropriate
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 % (30895)Memory used [KB]: 803
% 0.15/0.39 % (30897)Memory used [KB]: 803
% 0.15/0.39 % (30894)Memory used [KB]: 803
% 0.15/0.39 % (30895)Time elapsed: 0.003 s
% 0.15/0.39 % (30897)Time elapsed: 0.003 s
% 0.15/0.39 % (30894)Time elapsed: 0.003 s
% 0.15/0.39 % (30895)Instructions burned: 3 (million)
% 0.15/0.39 % (30897)Instructions burned: 3 (million)
% 0.15/0.39 % (30894)Instructions burned: 3 (million)
% 0.15/0.39 % (30894)------------------------------
% 0.15/0.39 % (30894)------------------------------
% 0.15/0.39 % (30895)------------------------------
% 0.15/0.39 % (30895)------------------------------
% 0.15/0.39 % (30897)------------------------------
% 0.15/0.39 % (30897)------------------------------
% 0.15/0.39 % (30899)First to succeed.
% 0.15/0.39 % (30896)Also succeeded, but the first one will report.
% 0.15/0.39 % (30899)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30893"
% 0.15/0.40 % (30899)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (30899)------------------------------
% 0.15/0.40 % (30899)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40 % (30899)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (30899)Memory used [KB]: 845
% 0.15/0.40 % (30899)Time elapsed: 0.007 s
% 0.15/0.40 % (30899)Instructions burned: 9 (million)
% 0.15/0.40 % (30893)Success in time 0.022 s
%------------------------------------------------------------------------------