TSTP Solution File: DAT324^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT324^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 19:52:09 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 34 ( 3 unt; 19 typ; 0 def)
% Number of atoms : 174 ( 27 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 28 ( 10 ~; 2 |; 8 &; 0 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 41 ( 40 >; 1 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 2 con; 0-6 aty)
% Number of variables : 33 ( 0 ^ 18 !; 4 ?; 33 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/ind_types/list': $tType > $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
'type/nums/num': $tType ).
thf(type_def_8,type,
sK0: $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'type/ind_types/list': $tType > $tType ).
thf(func_def_2,type,
'const/sets/set_of_list':
!>[X0: $tType] : ( 'type/ind_types/list'(X0) > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/list_of_set':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/ind_types/list'(X0) ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_6,type,
'const/lists/LENGTH':
!>[X0: $tType] : ( 'type/ind_types/list'(X0) > 'type/nums/num' ) ).
thf(func_def_10,type,
sK1: sK0 > $o ).
thf(func_def_11,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_12,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
vOR: $o > $o > $o ).
thf(func_def_15,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f55,plain,
$false,
inference(unit_resulting_resolution,[],[f14,f15,f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) != $true )
| ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
& ( vAPP('type/ind_types/list'(X0),sTfun(X0,$o),'const/sets/set_of_list'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = X1 ) )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) != $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
=> ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
& ( vAPP('type/ind_types/list'(X0),sTfun(X0,$o),'const/sets/set_of_list'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = X1 ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
=> ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
& ( vAPP('type/ind_types/list'(X0),sTfun(X0,$o),'const/sets/set_of_list'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = X1 ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
=> ( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
& ( vAPP('type/ind_types/list'(X0),sTfun(X0,$o),'const/sets/set_of_list'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/LIST_OF_SET_PROPERTIES_') ).
thf(f15,plain,
vAPP('type/ind_types/list'(sK0),'type/nums/num','const/lists/LENGTH'(sK0),vAPP(sTfun(sK0,$o),'type/ind_types/list'(sK0),'const/sets/list_of_set'(sK0),sK1)) != vAPP(sTfun(sK0,$o),'type/nums/num','const/sets/CARD'(sK0),sK1),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ( vAPP('type/ind_types/list'(sK0),'type/nums/num','const/lists/LENGTH'(sK0),vAPP(sTfun(sK0,$o),'type/ind_types/list'(sK0),'const/sets/list_of_set'(sK0),sK1)) != vAPP(sTfun(sK0,$o),'type/nums/num','const/sets/CARD'(sK0),sK1) )
& ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12]) ).
thf(f12,plain,
( ? [X0: $tType,X1: X0 > $o] :
( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) != vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) )
=> ( ( vAPP('type/ind_types/list'(sK0),'type/nums/num','const/lists/LENGTH'(sK0),vAPP(sTfun(sK0,$o),'type/ind_types/list'(sK0),'const/sets/list_of_set'(sK0),sK1)) != vAPP(sTfun(sK0,$o),'type/nums/num','const/sets/CARD'(sK0),sK1) )
& ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
? [X0: $tType,X1: X0 > $o] :
( ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) != vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
=> ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
=> ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
inference(rectify,[],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
=> ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
inference(negated_conjecture,[],[f2]) ).
thf(f2,conjecture,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
=> ( vAPP('type/ind_types/list'(X0),'type/nums/num','const/lists/LENGTH'(X0),vAPP(sTfun(X0,$o),'type/ind_types/list'(X0),'const/sets/list_of_set'(X0),X1)) = vAPP(sTfun(X0,$o),'type/nums/num','const/sets/CARD'(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/LENGTH_LIST_OF_SET_') ).
thf(f14,plain,
$true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : DAT324^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n002.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 : Sun May 19 23:09:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (7935)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (7940)WARNING: value z3 for option sas not known
% 0.14/0.38 % (7938)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (7939)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (7941)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (7940)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)
% 0.14/0.38 % (7943)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)
% 0.14/0.38 % (7944)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)
% 0.14/0.38 % Exception at run slice level% Exception at run slice level
% 0.14/0.38
% 0.14/0.38 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % (7944)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38 % (7942)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)
% 0.14/0.38 % (7944)First to succeed.
% 0.14/0.39 % (7940)Also succeeded, but the first one will report.
% 0.14/0.39 % (7943)Also succeeded, but the first one will report.
% 0.14/0.39 % (7944)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7935"
% 0.14/0.39 % (7944)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (7944)------------------------------
% 0.14/0.39 % (7944)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (7944)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (7944)Memory used [KB]: 764
% 0.14/0.39 % (7944)Time elapsed: 0.005 s
% 0.14/0.39 % (7944)Instructions burned: 5 (million)
% 0.14/0.39 % (7935)Success in time 0.02 s
%------------------------------------------------------------------------------