TSTP Solution File: DAT082_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT082_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 : n009.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 19:51:22 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 70
% Syntax : Number of formulae : 153 ( 54 unt; 18 typ; 0 def)
% Number of atoms : 357 ( 115 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 337 ( 115 ~; 113 |; 67 &)
% ( 39 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 294 ( 57 atm; 28 fun; 72 num; 137 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 29 ( 16 >; 13 *; 0 +; 0 <<)
% Number of predicates : 36 ( 31 usr; 28 prp; 0-2 aty)
% Number of functors : 18 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 239 ( 195 !; 44 ?; 239 :)
% 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_12,type,
sK2: ( $int * list ) > $int ).
tff(func_def_13,type,
sK3: ( $int * list ) > list ).
tff(func_def_14,type,
sK4: ( $int * list ) > $int ).
tff(func_def_15,type,
sK5: ( $int * list ) > list ).
tff(func_def_16,type,
sK6: ( $int * list ) > $int ).
tff(func_def_17,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(f235,plain,
$false,
inference(avatar_sat_refutation,[],[f102,f106,f110,f115,f119,f123,f127,f131,f135,f139,f143,f147,f151,f155,f159,f163,f167,f173,f177,f181,f185,f189,f193,f197,f210,f214,f218,f234]) ).
tff(f234,plain,
( spl8_1
| ~ spl8_4
| ~ spl8_27 ),
inference(avatar_contradiction_clause,[],[f233]) ).
tff(f233,plain,
( $false
| spl8_1
| ~ spl8_4
| ~ spl8_27 ),
inference(evaluation,[],[f232]) ).
tff(f232,plain,
( ( 2 != $sum(2,0) )
| spl8_1
| ~ spl8_4
| ~ spl8_27 ),
inference(forward_demodulation,[],[f231,f114]) ).
tff(f114,plain,
( ( 0 = length(nil) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f112]) ).
tff(f112,plain,
( spl8_4
<=> ( 0 = length(nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
tff(f231,plain,
( ( 2 != $sum(2,length(nil)) )
| spl8_1
| ~ spl8_27 ),
inference(evaluation,[],[f230]) ).
tff(f230,plain,
( ( 2 != $sum(1,$sum(1,length(nil))) )
| spl8_1
| ~ spl8_27 ),
inference(forward_demodulation,[],[f229,f217]) ).
tff(f217,plain,
( ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) )
| ~ spl8_27 ),
inference(avatar_component_clause,[],[f216]) ).
tff(f216,plain,
( spl8_27
<=> ! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
tff(f229,plain,
( ( 2 != $sum(1,length(cons(2,nil))) )
| spl8_1
| ~ spl8_27 ),
inference(superposition,[],[f101,f217]) ).
tff(f101,plain,
( ( 2 != length(cons(1,cons(2,nil))) )
| spl8_1 ),
inference(avatar_component_clause,[],[f99]) ).
tff(f99,plain,
( spl8_1
<=> ( 2 = length(cons(1,cons(2,nil))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
tff(f218,plain,
spl8_27,
inference(avatar_split_clause,[],[f69,f216]) ).
tff(f69,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: list] : ( length(cons(X0,X1)) = $sum(1,length(X1)) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X3: $int,X4: list] : ( length(cons(X3,X4)) = $sum(1,length(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_1) ).
tff(f214,plain,
spl8_26,
inference(avatar_split_clause,[],[f26,f212]) ).
tff(f212,plain,
( spl8_26
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f210,plain,
spl8_25,
inference(avatar_split_clause,[],[f25,f208]) ).
tff(f208,plain,
( spl8_25
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f197,plain,
spl8_24,
inference(avatar_split_clause,[],[f93,f195]) ).
tff(f195,plain,
( spl8_24
<=> ! [X2: $int,X0: $int,X3: list] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
tff(f93,plain,
! [X2: $int,X3: list,X0: $int] :
( sP1(X0,cons(X2,X3))
| ~ in(X0,X3) ),
inference(equality_resolution,[],[f85]) ).
tff(f85,plain,
! [X2: $int,X3: list,X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X3)
| ( cons(X2,X3) != X1 ) ),
inference(cnf_transformation,[],[f59]) ).
tff(f59,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])],[f56,f58,f57]) ).
tff(f57,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(f58,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(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 ) ) ) )
& ( ? [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,[],[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(flattening,[],[f54]) ).
tff(f54,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,[],[f45]) ).
tff(f45,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(f193,plain,
spl8_23,
inference(avatar_split_clause,[],[f79,f191]) ).
tff(f191,plain,
( spl8_23
<=> ! [X0: $int,X1: list] :
( in(X0,X1)
| ~ $less(0,count(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
tff(f79,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
| ~ $less(0,count(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ $less(0,count(X0,X1)) )
& ( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f36,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/sandbox/benchmark/theBenchmark.p',a_8) ).
tff(f189,plain,
spl8_22,
inference(avatar_split_clause,[],[f78,f187]) ).
tff(f187,plain,
( spl8_22
<=> ! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
tff(f78,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tff(f185,plain,
spl8_21,
inference(avatar_split_clause,[],[f30,f183]) ).
tff(f183,plain,
( spl8_21
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
tff(f30,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f181,plain,
spl8_20,
inference(avatar_split_clause,[],[f28,f179]) ).
tff(f179,plain,
( spl8_20
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f177,plain,
( spl8_19
| ~ spl8_3
| ~ spl8_15 ),
inference(avatar_split_clause,[],[f168,f157,f108,f175]) ).
tff(f175,plain,
( spl8_19
<=> ! [X0: $int] : inRange(X0,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
tff(f108,plain,
( spl8_3
<=> ! [X0: $int] : sP0(X0,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
tff(f157,plain,
( spl8_15
<=> ! [X0: $int,X1: list] :
( inRange(X0,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
tff(f168,plain,
( ! [X0: $int] : inRange(X0,nil)
| ~ spl8_3
| ~ spl8_15 ),
inference(resolution,[],[f158,f109]) ).
tff(f109,plain,
( ! [X0: $int] : sP0(X0,nil)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f108]) ).
tff(f158,plain,
( ! [X0: $int,X1: list] :
( ~ sP0(X0,X1)
| inRange(X0,X1) )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f157]) ).
tff(f173,plain,
spl8_18,
inference(avatar_split_clause,[],[f19,f171]) ).
tff(f171,plain,
( spl8_18
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
tff(f19,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f167,plain,
spl8_17,
inference(avatar_split_clause,[],[f87,f165]) ).
tff(f165,plain,
( spl8_17
<=> ! [X0: $int,X1: list] :
( in(X0,X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
tff(f87,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tff(f60,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f37,f45]) ).
tff(f37,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/sandbox/benchmark/theBenchmark.p',in_conv) ).
tff(f163,plain,
spl8_16,
inference(avatar_split_clause,[],[f86,f161]) ).
tff(f161,plain,
( spl8_16
<=> ! [X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
tff(f86,plain,
! [X0: $int,X1: list] :
( sP1(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tff(f159,plain,
spl8_15,
inference(avatar_split_clause,[],[f77,f157]) ).
tff(f77,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: $int,X1: list] :
( ( inRange(X0,X1)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
inference(nnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: $int,X1: list] :
( inRange(X0,X1)
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f35,f43]) ).
tff(f43,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(f35,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,[],[f17]) ).
tff(f17,plain,
! [X5: $int,X1: list] :
( inRange(X5,X1)
<=> ( ? [X0: $int,X4: list] :
( inRange(X5,X4)
& $less(X0,X5)
& ~ $less(X0,0)
& ( cons(X0,X4) = X1 ) )
| ( nil = X1 ) ) ),
inference(theory_normalization,[],[f6]) ).
tff(f6,axiom,
! [X5: $int,X1: list] :
( inRange(X5,X1)
<=> ( ? [X0: $int,X4: list] :
( inRange(X5,X4)
& $less(X0,X5)
& $lesseq(0,X0)
& ( cons(X0,X4) = X1 ) )
| ( nil = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f155,plain,
spl8_14,
inference(avatar_split_clause,[],[f76,f153]) ).
tff(f153,plain,
( spl8_14
<=> ! [X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
tff(f76,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tff(f151,plain,
spl8_13,
inference(avatar_split_clause,[],[f68,f149]) ).
tff(f149,plain,
( spl8_13
<=> ! [X0: $int,X1: list] : ( head(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
tff(f68,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(f147,plain,
spl8_12,
inference(avatar_split_clause,[],[f67,f145]) ).
tff(f145,plain,
( spl8_12
<=> ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
tff(f67,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/sandbox/benchmark/theBenchmark.p',l2) ).
tff(f143,plain,
spl8_11,
inference(avatar_split_clause,[],[f23,f141]) ).
tff(f141,plain,
( spl8_11
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
tff(f23,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f139,plain,
spl8_10,
inference(avatar_split_clause,[],[f95,f137]) ).
tff(f137,plain,
( spl8_10
<=> ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
tff(f95,plain,
! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
inference(equality_resolution,[],[f94]) ).
tff(f94,plain,
! [X1: list,X4: $int,X5: list] :
( sP1(X4,X1)
| ( cons(X4,X5) != X1 ) ),
inference(equality_resolution,[],[f84]) ).
tff(f84,plain,
! [X0: $int,X1: list,X4: $int,X5: list] :
( sP1(X0,X1)
| ( X0 != X4 )
| ( cons(X4,X5) != X1 ) ),
inference(cnf_transformation,[],[f59]) ).
tff(f135,plain,
spl8_9,
inference(avatar_split_clause,[],[f66,f133]) ).
tff(f133,plain,
( spl8_9
<=> ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
tff(f66,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(f131,plain,
spl8_8,
inference(avatar_split_clause,[],[f64,f129]) ).
tff(f129,plain,
( spl8_8
<=> ! [X0: list] : ( append(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
tff(f64,plain,
! [X0: list] : ( append(nil,X0) = X0 ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: list] : ( append(nil,X0) = X0 ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X1: list] : ( append(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).
tff(f127,plain,
spl8_7,
inference(avatar_split_clause,[],[f63,f125]) ).
tff(f125,plain,
( spl8_7
<=> ! [X0: $int] : ( 0 = count(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
tff(f63,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: $int] : ( 0 = count(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(f123,plain,
spl8_6,
inference(avatar_split_clause,[],[f29,f121]) ).
tff(f121,plain,
( spl8_6
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
tff(f29,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f119,plain,
spl8_5,
inference(avatar_split_clause,[],[f21,f117]) ).
tff(f117,plain,
( spl8_5
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
tff(f21,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f115,plain,
spl8_4,
inference(avatar_split_clause,[],[f62,f112]) ).
tff(f62,plain,
0 = length(nil),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
0 = length(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(f110,plain,
spl8_3,
inference(avatar_split_clause,[],[f92,f108]) ).
tff(f92,plain,
! [X0: $int] : sP0(X0,nil),
inference(equality_resolution,[],[f74]) ).
tff(f74,plain,
! [X0: $int,X1: list] :
( sP0(X0,X1)
| ( nil != X1 ) ),
inference(cnf_transformation,[],[f51]) ).
tff(f51,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,sK3(X0,X1))
& $less(sK2(X0,X1),X0)
& ~ $less(sK2(X0,X1),0)
& ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) )
| ( nil = X1 )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f49,f50]) ).
tff(f50,plain,
! [X0: $int,X1: list] :
( ? [X4: $int,X5: list] :
( inRange(X0,X5)
& $less(X4,X0)
& ~ $less(X4,0)
& ( cons(X4,X5) = X1 ) )
=> ( inRange(X0,sK3(X0,X1))
& $less(sK2(X0,X1),X0)
& ~ $less(sK2(X0,X1),0)
& ( cons(sK2(X0,X1),sK3(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f49,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,[],[f48]) ).
tff(f48,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,[],[f47]) ).
tff(f47,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,[],[f43]) ).
tff(f106,plain,
spl8_2,
inference(avatar_split_clause,[],[f24,f104]) ).
tff(f104,plain,
( spl8_2
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
tff(f24,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f102,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f61,f99]) ).
tff(f61,plain,
2 != length(cons(1,cons(2,nil))),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
2 != length(cons(1,cons(2,nil))),
inference(flattening,[],[f16]) ).
tff(f16,negated_conjecture,
( ~ 2 = length(cons(1,cons(2,nil))) ),
inference(negated_conjecture,[],[f15]) ).
tff(f15,conjecture,
2 = length(cons(1,cons(2,nil))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT082_1 : TPTP v8.2.0. Released v6.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n009.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 : Sun May 19 23:12:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (28103)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (28106)WARNING: value z3 for option sas not known
% 0.15/0.37 % (28107)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (28106)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)
% 0.15/0.37 % (28104)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (28108)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)
% 0.15/0.37 % (28109)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)
% 0.15/0.37 % (28110)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)
% 0.15/0.37 % (28105)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (28107)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.37 % (28107)Terminated due to inappropriate strategy.
% 0.15/0.37 % (28107)------------------------------
% 0.15/0.37 % (28107)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.37 % (28107)Termination reason: Inappropriate
% 0.15/0.37
% 0.15/0.37 % (28107)Memory used [KB]: 803
% 0.15/0.37 % (28107)Time elapsed: 0.003 s
% 0.15/0.37 % (28104)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.37 % (28107)Instructions burned: 3 (million)
% 0.15/0.37 % (28104)Terminated due to inappropriate strategy.
% 0.15/0.37 % (28104)------------------------------
% 0.15/0.37 % (28104)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.37 % (28104)Termination reason: Inappropriate
% 0.15/0.37
% 0.15/0.37 % (28104)Memory used [KB]: 803
% 0.15/0.37 % (28104)Time elapsed: 0.003 s
% 0.15/0.37 % (28104)Instructions burned: 3 (million)
% 0.15/0.37 % (28105)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.37 % (28107)------------------------------
% 0.15/0.37 % (28107)------------------------------
% 0.15/0.37 % (28105)Terminated due to inappropriate strategy.
% 0.15/0.37 % (28105)------------------------------
% 0.15/0.37 % (28105)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.37 % (28105)Termination reason: Inappropriate
% 0.15/0.37
% 0.15/0.37 % (28105)Memory used [KB]: 803
% 0.15/0.37 % (28105)Time elapsed: 0.003 s
% 0.15/0.37 % (28105)Instructions burned: 3 (million)
% 0.15/0.37 % (28104)------------------------------
% 0.15/0.37 % (28104)------------------------------
% 0.15/0.37 % (28105)------------------------------
% 0.15/0.37 % (28105)------------------------------
% 0.15/0.38 % (28108)First to succeed.
% 0.15/0.38 % (28108)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28103"
% 0.15/0.38 % (28108)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38 % (28108)------------------------------
% 0.15/0.38 % (28108)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38 % (28108)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (28108)Memory used [KB]: 890
% 0.15/0.38 % (28108)Time elapsed: 0.010 s
% 0.15/0.38 % (28108)Instructions burned: 11 (million)
% 0.15/0.38 % (28103)Success in time 0.025 s
%------------------------------------------------------------------------------