TSTP Solution File: SEV476^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV476^1 : 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 : n021.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 May 21 04:15:52 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 43 ( 10 unt; 14 typ; 0 def)
% Number of atoms : 278 ( 43 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 53 ( 24 ~; 14 |; 7 &; 0 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 71 ( 70 >; 1 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 2 con; 0-6 aty)
% Number of variables : 68 ( 0 ^ 53 !; 6 ?; 68 :)
% ( 9 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/DIFF':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_6,type,
sK1: sK0 > $o ).
thf(func_def_7,type,
sK2: sK0 > $o ).
thf(func_def_9,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_10,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
vOR: $o > $o > $o ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f84,plain,
$false,
inference(trivial_inequality_removal,[],[f78]) ).
thf(f78,plain,
$true != $true,
inference(superposition,[],[f77,f18]) ).
thf(f18,plain,
$true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
( ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK1),sK2)) )
& ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f16]) ).
thf(f16,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)) != $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) )
=> ( ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK1),sK2)) )
& ( $true = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)) != $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
=> ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)) = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_DIFF_') ).
thf(f77,plain,
$true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),sK1),
inference(equality_resolution,[],[f75]) ).
thf(f75,plain,
! [X0: sK0 > $o,X1: sK0 > $o] :
( ( vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK1),sK2) != vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),X0),X1) )
| ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),X0) ) ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f74,plain,
! [X0: sK0 > $o,X1: sK0 > $o] :
( ( $true = $false )
| ( $true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),X0) )
| ( vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK1),sK2) != vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),X0),X1) ) ),
inference(constrained_superposition,[],[f52,f70]) ).
thf(f70,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)) = $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) != $true ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f69,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $true != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)) = $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) != $true ) ),
inference(superposition,[],[f20,f21]) ).
thf(f21,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)),X1) = $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)),X1) = $true ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)),X1),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),'const/sets/DIFF'(X0),X1),X2)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_DIFF_') ).
thf(f20,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(flattening,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) = $true ) )
=> ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) )
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) )
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(f52,plain,
$false = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK1),sK2)),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| ( $false = vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK1),sK2)) ) ),
inference(superposition,[],[f19,f6]) ).
thf(f6,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f19,plain,
$true != vAPP(sTfun(sK0,$o),$o,'const/sets/FINITE'(sK0),vAPP(sTfun(sK0,$o),sTfun(sK0,$o),vAPP(sTfun(sK0,$o),sTfun(sTfun(sK0,$o),sTfun(sK0,$o)),'const/sets/DIFF'(sK0),sK1),sK2)),
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV476^1 : TPTP v8.2.0. Released v7.0.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n021.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun May 19 18:50:53 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.31 % (15966)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32 % (15972)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.32 % (15968)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.32 % (15967)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.32 % (15971)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.32 % (15970)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.32 % (15969)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.15/0.32 % (15973)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.32 % (15970)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.32 % (15969)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.32 % Exception at run slice level% Exception at run slice level
% 0.15/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.32
% 0.15/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% Exception at run slice level
% 0.15/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.32
% 0.15/0.33 % Exception at run slice level
% 0.15/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.33 % (15969)First to succeed.
% 0.15/0.33 % (15971)Also succeeded, but the first one will report.
% 0.15/0.33 % (15969)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15966"
% 0.15/0.33 % (15972)Also succeeded, but the first one will report.
% 0.15/0.33 % (15969)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.33 % (15969)------------------------------
% 0.15/0.33 % (15969)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.33 % (15969)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (15969)Memory used [KB]: 780
% 0.15/0.33 % (15969)Time elapsed: 0.006 s
% 0.15/0.33 % (15969)Instructions burned: 8 (million)
% 0.15/0.33 % (15966)Success in time 0.019 s
%------------------------------------------------------------------------------