%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP376_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:33:44 AM UTC 2026
% Result : Theorem 8.31s 2.10s
% Output : Refutation 8.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 31 ~; 22 |; 5 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number arithmetic : 165 ( 58 atm; 18 fun; 68 num; 21 var)
% Number of types : 36 ( 33 usr; 2 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 3 prp; 0-3 aty)
% Number of functors : 82 ( 78 usr; 25 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Real_real_bool_fun_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'Real_num_fun$': $tType ).
tff(type_def_8,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_9,type,
'A_ltln_list$': $tType ).
tff(type_def_10,type,
'Num_num_fun$': $tType ).
tff(type_def_11,type,
'Nat_enat_fun$': $tType ).
tff(type_def_12,type,
'Int_real_fun$': $tType ).
tff(type_def_13,type,
'Num_enat_fun$': $tType ).
tff(type_def_14,type,
'Enat$': $tType ).
tff(type_def_15,type,
'Int_int_fun$': $tType ).
tff(type_def_16,type,
'Enat_int_fun$': $tType ).
tff(type_def_17,type,
'Num_bool_fun$': $tType ).
tff(type_def_18,type,
'Nat_nat_fun$': $tType ).
tff(type_def_19,type,
'Num_real_fun$': $tType ).
tff(type_def_20,type,
'Nat$': $tType ).
tff(type_def_21,type,
'Num$': $tType ).
tff(type_def_22,type,
tlbool: $tType ).
tff(type_def_23,type,
'Enat_bool_fun$': $tType ).
tff(type_def_24,type,
'Int_enat_fun$': $tType ).
tff(type_def_25,type,
'Nat_num_fun$': $tType ).
tff(type_def_26,type,
'Enat_num_fun$': $tType ).
tff(type_def_27,type,
'Nat_real_fun$': $tType ).
tff(type_def_28,type,
'Real_int_fun$': $tType ).
tff(type_def_29,type,
'Enat_enat_bool_fun_fun$': $tType ).
tff(type_def_30,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_31,type,
'Nat_bool_fun$': $tType ).
tff(type_def_32,type,
'Real_bool_fun$': $tType ).
tff(type_def_33,type,
'Real_set$': $tType ).
tff(type_def_34,type,
'Nat_int_fun$': $tType ).
tff(type_def_35,type,
'Int_num_fun$': $tType ).
tff(type_def_36,type,
'Num_int_fun$': $tType ).
tff(type_def_37,type,
'Num_num_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'less_eq$': 'Num_num_bool_fun_fun$' ).
tff(func_def_1,type,
'less_eq$a': 'Enat_enat_bool_fun_fun$' ).
tff(func_def_2,type,
'fun_app$p': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_3,type,
'dbl$': 'Int_int_fun$' ).
tff(func_def_4,type,
'zero$': 'Nat$' ).
tff(func_def_5,type,
'zero$a': 'Enat$' ).
tff(func_def_6,type,
'numeral$b': 'Num_real_fun$' ).
tff(func_def_7,type,
'power$c': $real > 'Nat_real_fun$' ).
tff(func_def_8,type,
'n$': 'Nat$' ).
tff(func_def_9,type,
'size$a': 'Num$' > 'Nat$' ).
tff(func_def_10,type,
'of_nat$a': 'Nat_nat_fun$' ).
tff(func_def_11,type,
'fun_app$z': ( 'Int_real_fun$' * $int ) > $real ).
tff(func_def_12,type,
'times$b': $int > 'Int_int_fun$' ).
tff(func_def_13,type,
'fun_app$v': ( 'Int_num_fun$' * $int ) > 'Num$' ).
tff(func_def_14,type,
'fun_app$f': ( 'Num_num_bool_fun_fun$' * 'Num$' ) > 'Num_bool_fun$' ).
tff(func_def_15,type,
'ys$': 'A_ltln_list$' ).
tff(func_def_16,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_17,type,
'times$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_18,type,
'less$': 'Num_num_bool_fun_fun$' ).
tff(func_def_19,type,
'dbl$a': $real > $real ).
tff(func_def_20,type,
'less_eq$b': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_21,type,
tltrue: tlbool ).
tff(func_def_22,type,
'fun_app$w': ( 'Enat_num_fun$' * 'Enat$' ) > 'Num$' ).
tff(func_def_23,type,
'uu$': 'Real_set$' > 'Real_bool_fun$' ).
tff(func_def_24,type,
'fun_app$j': ( 'Num_real_fun$' * 'Num$' ) > $real ).
tff(func_def_25,type,
'fun_app$r': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_26,type,
'fun_app$a': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_27,type,
'pow$': 'Num$' > 'Num_num_fun$' ).
tff(func_def_28,type,
'numeral$c': 'Num$' > 'Nat$' ).
tff(func_def_29,type,
'fun_app$m': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).
tff(func_def_30,type,
'less$a': 'Enat_enat_bool_fun_fun$' ).
tff(func_def_31,type,
'power$a': $int > 'Nat_int_fun$' ).
tff(func_def_32,type,
'fun_app$x': ( 'Real_num_fun$' * $real ) > 'Num$' ).
tff(func_def_33,type,
'numeral$': 'Num_int_fun$' ).
tff(func_def_34,type,
'power$b': 'Enat$' > 'Nat_enat_fun$' ).
tff(func_def_35,type,
'numeral$a': 'Num_enat_fun$' ).
tff(func_def_36,type,
'fun_app$s': ( 'Real_real_bool_fun_fun$' * $real ) > 'Real_bool_fun$' ).
tff(func_def_37,type,
'fun_app$i': ( 'Num_enat_fun$' * 'Num$' ) > 'Enat$' ).
tff(func_def_38,type,
'times$c': ( 'Enat$' * 'Enat$' ) > 'Enat$' ).
tff(func_def_39,type,
'fun_app$t': ( 'Enat_int_fun$' * 'Enat$' ) > $int ).
tff(func_def_40,type,
'one$': 'Num$' ).
tff(func_def_41,type,
'fun_app$d': ( 'Num_int_fun$' * 'Num$' ) > $int ).
tff(func_def_42,type,
'less$b': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_43,type,
tlfalse: tlbool ).
tff(func_def_44,type,
'nat$': $int > 'Nat$' ).
tff(func_def_45,type,
'fun_app$u': ( 'Real_int_fun$' * $real ) > $int ).
tff(func_def_46,type,
'fun_app$o': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_47,type,
'fun_app$c': ( 'Num_num_fun$' * 'Num$' ) > 'Num$' ).
tff(func_def_48,type,
'fun_app$l': ( 'Nat_enat_fun$' * 'Nat$' ) > 'Enat$' ).
tff(func_def_49,type,
'size$': 'A_ltln_list$' > 'Nat$' ).
tff(func_def_50,type,
'of_nat$c': 'Nat_enat_fun$' ).
tff(func_def_51,type,
'fun_app$k': ( 'Nat_num_fun$' * 'Nat$' ) > 'Num$' ).
tff(func_def_52,type,
'fun_app$h': ( 'Enat_enat_bool_fun_fun$' * 'Enat$' ) > 'Enat_bool_fun$' ).
tff(func_def_53,type,
'times$a': 'Num$' > 'Num_num_fun$' ).
tff(func_def_54,type,
'of_nat$b': 'Nat_real_fun$' ).
tff(func_def_55,type,
'fun_app$y': ( 'Int_enat_fun$' * $int ) > 'Enat$' ).
tff(func_def_56,type,
'times$d': ( $real * $real ) > $real ).
tff(func_def_57,type,
'collect$': 'Real_bool_fun$' > 'Real_set$' ).
tff(func_def_58,type,
'power$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_59,type,
'bit0$': 'Num_num_fun$' ).
tff(func_def_60,type,
'fun_app$b': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_70,type,
sK3: $int > 'Nat$' ).
tff(func_def_71,type,
sK4: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_72,type,
sK5: 'Nat$' > 'Nat$' ).
tff(func_def_73,type,
sK6: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_74,type,
sK7: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_75,type,
sK8: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_76,type,
sK9: $int > 'Nat$' ).
tff(func_def_77,type,
sK10: 'Nat$' > 'Nat$' ).
tff(func_def_78,type,
sK11: $int > 'Nat$' ).
tff(func_def_79,type,
sK12: 'Nat$' > 'Nat$' ).
tff(func_def_80,type,
sK13: $int > 'Nat$' ).
tff(func_def_81,type,
sK14: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_82,type,
sK15: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_83,type,
sK16: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_84,type,
sK17: 'Nat$' > 'Nat$' ).
tff(func_def_85,type,
sK18: 'Nat$' > 'Nat$' ).
tff(func_def_86,type,
sK19: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(pred_def_1,type,
'fun_app$q': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_2,type,
'fun_app$n': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_3,type,
'fun_app$': ( 'Real_bool_fun$' * $real ) > $o ).
tff(pred_def_4,type,
'fun_app$e': ( 'Num_bool_fun$' * 'Num$' ) > $o ).
tff(pred_def_5,type,
'member$': ( $real * 'Real_set$' ) > $o ).
tff(pred_def_6,type,
'fun_app$g': ( 'Enat_bool_fun$' * 'Enat$' ) > $o ).
tff(pred_def_11,type,
sP0: ( $int * $int * $int ) > $o ).
tff(pred_def_12,type,
sP1: ( $int * $int * $int ) > $o ).
tff(pred_def_13,type,
sP2: ( $int * $int * $int ) > $o ).
tff(f2,conjecture,
$lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$'))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture1) ).
tff(f3,negated_conjecture,
~ $lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$'))),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,axiom,
$lesseq('fun_app$a'('of_nat$','size$'('ys$')),'fun_app$a'('of_nat$','n$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
tff(f230,axiom,
! [X0: $int,X2: $int,X1: $int] :
( ( $lesseq(X0,X1)
& $lesseq(X1,X2) )
=> $lesseq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).
tff(f587,axiom,
! [X1: 'Nat$',X2: 'Nat$',X0: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2)))
& $less(0,'fun_app$a'('of_nat$',X0)) )
=> $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom585) ).
tff(f606,axiom,
! [X0: 'Nat$'] : $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom604) ).
tff(f637,axiom,
! [X0: 'Nat$'] : $lesseq(0,'fun_app$a'('of_nat$',X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom635) ).
tff(f701,plain,
~ ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$')))),
inference(theory_normalization,[],[f3]) ).
tff(f755,plain,
~ $less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$'))),
inference(theory_normalization,[],[f4]) ).
tff(f816,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$a'('of_nat$',X0),0),
inference(theory_normalization,[],[f637]) ).
tff(f828,plain,
! [X0: $int,X2: $int,X1: $int] :
( ( ~ $less(X1,X0)
& ~ $less(X2,X1) )
=> ~ $less(X2,X0) ),
inference(theory_normalization,[],[f230]) ).
tff(f848,plain,
$less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$')))),
inference(flattening,[],[f701]) ).
tff(f851,plain,
! [X0: $int,X2: $int,X1: $int] :
( ( ~ $less(X2,X0)
& ~ $less(X1,X2) )
=> ~ $less(X1,X0) ),
inference(rectify,[],[f828]) ).
tff(f897,plain,
! [X0: 'Nat$',X2: 'Nat$',X1: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1)))
& $less(0,'fun_app$a'('of_nat$',X2)) )
=> $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(rectify,[],[f587]) ).
tff(f950,plain,
! [X0: $int,X2: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X2,X0)
| $less(X1,X2) ),
inference(ennf_transformation,[],[f851]) ).
tff(f951,plain,
! [X1: $int,X2: $int,X0: $int] :
( $less(X1,X2)
| $less(X2,X0)
| ~ $less(X1,X0) ),
inference(flattening,[],[f950]) ).
tff(f1039,plain,
! [X0: 'Nat$',X2: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X2)) ),
inference(ennf_transformation,[],[f897]) ).
tff(f1040,plain,
! [X0: 'Nat$',X2: 'Nat$',X1: 'Nat$'] :
( ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1))) ),
inference(flattening,[],[f1039]) ).
tff(f1074,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less(0,'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X0)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) ),
inference(rectify,[],[f1040]) ).
tff(f1090,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,X1)
| $less(X1,X2)
| ~ $less(X0,X2) ),
inference(rectify,[],[f951]) ).
tff(f1235,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X0)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) ),
inference(cnf_transformation,[],[f1074]) ).
tff(f1256,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X2)
| $less(X0,X1)
| ~ $less(X0,X2) ),
inference(cnf_transformation,[],[f1090]) ).
tff(f1302,plain,
$less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$')))),
inference(cnf_transformation,[],[f848]) ).
tff(f1373,plain,
! [X0: 'Nat$'] : $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),X0))),
inference(cnf_transformation,[],[f606]) ).
tff(f1401,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$a'('of_nat$',X0),0),
inference(cnf_transformation,[],[f816]) ).
tff(f1411,plain,
~ $less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$'))),
inference(cnf_transformation,[],[f755]) ).
tff(f1477,definition,
( spl20_1
<=> $less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$')))) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
tff(f1479,plain,
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))))
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f1477]) ).
tff(f1480,plain,
spl20_1,
inference(avatar_split_clause,[],[f1302,f1477]) ).
tff(f1481,plain,
( ~ $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))))
| ~ spl20_1 ),
inference(unit_resulting_resolution,[],[f1235,f1411,f1479]) ).
tff(f1871,definition,
( spl20_16
<=> $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1)))))) ),
introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition]) ).
tff(f1873,plain,
( ~ $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))))
| spl20_16 ),
inference(avatar_component_clause,[],[f1871]) ).
tff(f1874,plain,
( ~ spl20_16
| ~ spl20_1 ),
inference(avatar_split_clause,[],[f1481,f1477,f1871]) ).
tff(f3118,plain,
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1)))),0)
| spl20_16 ),
inference(unit_resulting_resolution,[],[f1256,f1373,f1873]) ).
tff(f3328,plain,
( $false
| spl20_16 ),
inference(forward_subsumption_resolution,[],[f3118,f1401]) ).
tff(f3329,plain,
spl20_16,
inference(avatar_contradiction_clause,[],[f3328]) ).
tff(f3331,plain,
$false,
inference(avatar_smt_refutation,[],[f3329,f1874,f1480]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP376_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 12:56:07 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.32/1.43 % (3494065)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.32/1.43 % (3494076)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1825242349:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.32/1.43 % (3494076)Instruction limit reached!
% 3.32/1.43 % (3494076)------------------------------
% 3.32/1.43 % (3494076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.43 % (3494076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.43 % (3494076)CaDiCaL version: 2.1.3
% 3.32/1.43 % (3494076)Termination reason: Instruction limit
% 3.32/1.43 % (3494076)Termination phase: Preprocessing 3
% 3.32/1.43 % (3494076)Time elapsed: 0.011 s
% 3.32/1.43 % (3494076)Peak memory usage: 88 MB
% 3.32/1.43 % (3494076)Instructions burned: 36 (million)
% 3.32/1.43 % (3494070)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2223280945:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.32/1.43 % (3494071)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1824263558:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.32/1.43 % (3494072)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4286872936:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.32/1.43 % (3494074)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1914590757:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.32/1.43 % (3494073)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3240056040:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.32/1.43 % (3494075)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4048079107:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.32/1.43 % (3494074)Instruction limit reached!
% 3.32/1.43 % (3494074)------------------------------
% 3.32/1.43 % (3494074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.43 % (3494074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.43 % (3494074)CaDiCaL version: 2.1.3
% 3.32/1.43 % (3494074)Termination reason: Instruction limit
% 3.32/1.43 % (3494074)Termination phase: Property scanning
% 3.32/1.43 % (3494074)Time elapsed: 0.003 s
% 3.32/1.43 % (3494074)Peak memory usage: 85 MB
% 3.32/1.43 % (3494074)Instructions burned: 4 (million)
% 3.32/1.43 % (3494073)Instruction limit reached!
% 3.32/1.43 % (3494073)------------------------------
% 3.32/1.43 % (3494073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.43 % (3494073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.43 % (3494073)CaDiCaL version: 2.1.3
% 3.32/1.43 % (3494073)Termination reason: Instruction limit
% 3.32/1.43 % (3494073)Termination phase: Property scanning
% 3.32/1.43 % (3494073)Time elapsed: 0.004 s
% 3.32/1.43 % (3494073)Peak memory usage: 85 MB
% 3.32/1.43 % (3494073)Instructions burned: 7 (million)
% 3.32/1.43 % (3494070)Instruction limit reached!
% 3.32/1.43 % (3494070)------------------------------
% 3.32/1.43 % (3494070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.43 % (3494070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.43 % (3494070)CaDiCaL version: 2.1.3
% 3.32/1.43 % (3494070)Termination reason: Instruction limit
% 3.32/1.43 % (3494070)Termination phase: shuffling
% 3.32/1.43 % (3494070)Time elapsed: 0.007 s
% 3.32/1.43 % (3494070)Peak memory usage: 85 MB
% 3.32/1.43 % (3494070)Instructions burned: 12 (million)
% 3.32/1.43 % (3494075)Instruction limit reached!
% 3.32/1.43 % (3494075)------------------------------
% 3.32/1.43 % (3494075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.43 % (3494075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.43 % (3494075)CaDiCaL version: 2.1.3
% 3.32/1.43 % (3494075)Termination reason: Instruction limit
% 3.32/1.43 % (3494075)Termination phase: Property scanning
% 3.32/1.43 % (3494075)Time elapsed: 0.025 s
% 3.32/1.43 % (3494075)Peak memory usage: 87 MB
% 3.32/1.43 % (3494075)Instructions burned: 46 (million)
% 3.32/1.43 % (3494078)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3461321373:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.32/1.43 % (3494078)Instruction limit reached!
% 3.32/1.43 % (3494078)------------------------------
% 3.90/1.57 % (3494078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3494078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3494078)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3494078)Termination reason: Instruction limit
% 3.90/1.57 % (3494078)Termination phase: SInE selection
% 3.90/1.57 % (3494078)Time elapsed: 0.004 s
% 3.90/1.57 % (3494078)Peak memory usage: 86 MB
% 3.90/1.57 % (3494078)Instructions burned: 14 (million)
% 3.90/1.57 % (3494072)Instruction limit reached!
% 3.90/1.57 % (3494072)------------------------------
% 3.90/1.57 % (3494072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3494072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3494072)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3494072)Termination reason: Instruction limit
% 3.90/1.57 % (3494072)Termination phase: Saturation
% 3.90/1.57 % (3494072)Time elapsed: 0.149 s
% 3.90/1.57 % (3494072)Peak memory usage: 118 MB
% 3.90/1.57 % (3494072)Instructions burned: 201 (million)
% 3.90/1.57 % (3494086)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3210205948:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.90/1.57 % (3494085)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=1536164652:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.90/1.57 % (3494087)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=102408541:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.90/1.57 % (3494086)Instruction limit reached!
% 3.90/1.57 % (3494086)------------------------------
% 3.90/1.57 % (3494086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3494086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3494086)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3494086)Termination reason: Instruction limit
% 3.90/1.57 % (3494086)Termination phase: shuffling
% 3.90/1.57 % (3494086)Time elapsed: 0.010 s
% 3.90/1.57 % (3494086)Peak memory usage: 86 MB
% 3.90/1.57 % (3494086)Instructions burned: 17 (million)
% 3.90/1.57 % (3494087)Instruction limit reached!
% 3.90/1.57 % (3494087)------------------------------
% 3.90/1.57 % (3494087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3494087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3494087)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3494087)Termination reason: Instruction limit
% 3.90/1.57 % (3494087)Termination phase: Preprocessing 1
% 3.90/1.57 % (3494087)Time elapsed: 0.013 s
% 3.90/1.57 % (3494087)Peak memory usage: 86 MB
% 3.90/1.57 % (3494087)Instructions burned: 25 (million)
% 3.90/1.57 % (3494085)Instruction limit reached!
% 3.90/1.57 % (3494085)------------------------------
% 3.90/1.57 % (3494085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3494085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3494085)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3494085)Termination reason: Instruction limit
% 3.90/1.57 % (3494085)Termination phase: Preprocessing 3
% 3.90/1.57 % (3494085)Time elapsed: 0.016 s
% 3.90/1.57 % (3494085)Peak memory usage: 87 MB
% 3.90/1.57 % (3494085)Instructions burned: 29 (million)
% 3.90/1.57 % (3494088)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=348906919:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.90/1.57 % (3494090)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=567482197:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 3.90/1.57 % (3494088)Instruction limit reached!
% 3.90/1.57 % (3494088)------------------------------
% 3.90/1.57 % (3494088)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.90/1.57 % (3494088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.90/1.57 % (3494088)CaDiCaL version: 2.1.3
% 3.90/1.57 % (3494088)Termination reason: Instruction limit
% 3.90/1.57 % (3494088)Termination phase: Preprocessing 2
% 3.90/1.57 % (3494088)Time elapsed: 0.015 s
% 3.90/1.57 % (3494088)Peak memory usage: 86 MB
% 3.90/1.57 % (3494088)Instructions burned: 27 (million)
% 3.90/1.57 % (3494071)Instruction limit reached!
% 3.90/1.57 % (3494071)------------------------------
% 5.39/1.73 % (3494071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.73 % (3494071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.73 % (3494071)CaDiCaL version: 2.1.3
% 5.39/1.73 % (3494071)Termination reason: Instruction limit
% 5.39/1.73 % (3494071)Termination phase: Saturation
% 5.39/1.73 % (3494071)Time elapsed: 0.213 s
% 5.39/1.73 % (3494071)Peak memory usage: 119 MB
% 5.39/1.73 % (3494071)Instructions burned: 308 (million)
% 5.39/1.73 % (3494090)Instruction limit reached!
% 5.39/1.73 % (3494090)------------------------------
% 5.39/1.73 % (3494090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.73 % (3494090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.73 % (3494090)CaDiCaL version: 2.1.3
% 5.39/1.73 % (3494090)Termination reason: Instruction limit
% 5.39/1.73 % (3494090)Termination phase: Property scanning
% 5.39/1.73 % (3494090)Time elapsed: 0.024 s
% 5.39/1.73 % (3494090)Peak memory usage: 89 MB
% 5.39/1.73 % (3494090)Instructions burned: 90 (million)
% 5.39/1.73 % (3494094)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=3251714278:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 5.39/1.73 % (3494094)Instruction limit reached!
% 5.39/1.73 % (3494094)------------------------------
% 5.39/1.73 % (3494094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.73 % (3494094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.73 % (3494094)CaDiCaL version: 2.1.3
% 5.39/1.73 % (3494094)Termination reason: Instruction limit
% 5.39/1.73 % (3494094)Termination phase: shuffling
% 5.39/1.73 % (3494094)Time elapsed: 0.002 s
% 5.39/1.73 % (3494094)Peak memory usage: 85 MB
% 5.39/1.73 % (3494094)Instructions burned: 2 (million)
% 5.39/1.73 % (3494095)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=924908592:i=181:rtra=on:ss=axioms:ev=cautious_2996 on theBenchmark for (2996ds/181Mi)
% 5.39/1.73 % (3494096)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=2810658381:i=4:ep=RST:ins=2:rtra=on_2996 on theBenchmark for (2996ds/4Mi)
% 5.39/1.73 % (3494097)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=313229816:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2996 on theBenchmark for (2996ds/66Mi)
% 5.39/1.73 % (3494096)Instruction limit reached!
% 5.39/1.73 % (3494096)------------------------------
% 5.39/1.73 % (3494096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.73 % (3494096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.73 % (3494096)CaDiCaL version: 2.1.3
% 5.39/1.73 % (3494096)Termination reason: Instruction limit
% 5.39/1.73 % (3494096)Termination phase: Property scanning
% 5.39/1.73 % (3494096)Time elapsed: 0.003 s
% 5.39/1.73 % (3494096)Peak memory usage: 85 MB
% 5.39/1.73 % (3494096)Instructions burned: 4 (million)
% 5.39/1.73 % (3494102)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=2729404921:st=3:i=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/2Mi)
% 5.39/1.73 % (3494102)Instruction limit reached!
% 5.39/1.73 % (3494102)------------------------------
% 5.39/1.73 % (3494102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.73 % (3494102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.73 % (3494102)CaDiCaL version: 2.1.3
% 5.39/1.73 % (3494102)Termination reason: Instruction limit
% 5.39/1.73 % (3494102)Termination phase: Property scanning
% 5.39/1.73 % (3494102)Time elapsed: 0.002 s
% 5.39/1.73 % (3494102)Peak memory usage: 86 MB
% 5.39/1.73 % (3494100)lrs+10_1_thi=all:si=on:fd=off:random_seed=709508571:i=53:rtra=on:gtg=all_2995 on theBenchmark for (2995ds/53Mi)
% 5.39/1.73 % (3494102)Instructions burned: 6 (million)
% 5.39/1.73 % (3494097)Instruction limit reached!
% 5.39/1.73 % (3494097)------------------------------
% 5.39/1.73 % (3494097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.39/1.73 % (3494097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.39/1.73 % (3494097)CaDiCaL version: 2.1.3
% 5.39/1.73 % (3494097)Termination reason: Instruction limit
% 5.39/1.73 % (3494097)Termination phase: Property scanning
% 5.39/1.73 % (3494097)Time elapsed: 0.035 s
% 5.39/1.73 % (3494097)Peak memory usage: 88 MB
% 5.39/1.73 % (3494097)Instructions burned: 67 (million)
% 5.39/1.73 % (3494100)Instruction limit reached!
% 6.55/1.95 % (3494100)------------------------------
% 6.55/1.95 % (3494100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.95 % (3494100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.95 % (3494100)CaDiCaL version: 2.1.3
% 6.55/1.95 % (3494100)Termination reason: Instruction limit
% 6.55/1.95 % (3494100)Termination phase: Preprocessing 3
% 6.55/1.95 % (3494100)Time elapsed: 0.027 s
% 6.55/1.95 % (3494100)Peak memory usage: 87 MB
% 6.55/1.95 % (3494100)Instructions burned: 54 (million)
% 6.55/1.95 % (3494101)ott+1011_1_to=kbo:plsq=on:drc=off:si=on:plsqr=32,1:sp=const_frequency:sos=all:uwa=one_side_interpreted:sac=on:random_seed=3001080789:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2995 on theBenchmark for (2995ds/8Mi)
% 6.55/1.95 % (3494101)Instruction limit reached!
% 6.55/1.95 % (3494101)------------------------------
% 6.55/1.95 % (3494101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.95 % (3494101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.95 % (3494101)CaDiCaL version: 2.1.3
% 6.55/1.95 % (3494101)Termination reason: Instruction limit
% 6.55/1.95 % (3494101)Termination phase: shuffling
% 6.55/1.95 % (3494101)Time elapsed: 0.005 s
% 6.55/1.95 % (3494101)Peak memory usage: 85 MB
% 6.55/1.95 % (3494101)Instructions burned: 10 (million)
% 6.55/1.95 % (3494104)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=3265291357:i=2:doe=on:canc=force:asg=cautious:rtra=on_2995 on theBenchmark for (2995ds/2Mi)
% 6.55/1.95 % (3494111)dis+10_1_si=on:random_seed=1686585818:i=10:ep=R:rtra=on_2994 on theBenchmark for (2994ds/10Mi)
% 6.55/1.95 % (3494095)Instruction limit reached!
% 6.55/1.95 % (3494095)------------------------------
% 6.55/1.95 % (3494095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.95 % (3494095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.95 % (3494095)CaDiCaL version: 2.1.3
% 6.55/1.95 % (3494095)Termination reason: Instruction limit
% 6.55/1.95 % (3494095)Termination phase: Saturation
% 6.55/1.95 % (3494095)Time elapsed: 0.123 s
% 6.55/1.95 % (3494095)Peak memory usage: 91 MB
% 6.55/1.95 % (3494095)Instructions burned: 182 (million)
% 6.55/1.95 % (3494104)Instruction limit reached!
% 6.55/1.95 % (3494104)------------------------------
% 6.55/1.95 % (3494104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.95 % (3494104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.95 % (3494104)CaDiCaL version: 2.1.3
% 6.55/1.95 % (3494104)Termination reason: Instruction limit
% 6.55/1.95 % (3494104)Termination phase: shuffling
% 6.55/1.95 % (3494104)Time elapsed: 0.002 s
% 6.55/1.95 % (3494104)Peak memory usage: 85 MB
% 6.55/1.95 % (3494104)Instructions burned: 2 (million)
% 6.55/1.95 % (3494111)Instruction limit reached!
% 6.55/1.95 % (3494111)------------------------------
% 6.55/1.95 % (3494111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.95 % (3494111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.95 % (3494111)CaDiCaL version: 2.1.3
% 6.55/1.95 % (3494111)Termination reason: Instruction limit
% 6.55/1.95 % (3494111)Termination phase: Property scanning
% 6.55/1.95 % (3494111)Time elapsed: 0.003 s
% 6.55/1.95 % (3494111)Peak memory usage: 85 MB
% 6.55/1.95 % (3494111)Instructions burned: 11 (million)
% 6.55/1.95 % (3494108)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=1687827617:i=127:doe=on:rtra=on_2994 on theBenchmark for (2994ds/127Mi)
% 6.55/1.95 % (3494112)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=1528783252:i=26:canc=cautious:av=off:rtra=on_2994 on theBenchmark for (2994ds/26Mi)
% 6.55/1.95 % (3494112)Instruction limit reached!
% 6.55/1.95 % (3494112)------------------------------
% 6.55/1.95 % (3494112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.95 % (3494112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.95 % (3494112)CaDiCaL version: 2.1.3
% 6.55/1.95 % (3494112)Termination reason: Instruction limit
% 6.55/1.95 % (3494112)Termination phase: shuffling
% 6.55/1.95 % (3494112)Time elapsed: 0.014 s
% 6.55/1.95 % (3494112)Peak memory usage: 86 MB
% 6.55/1.95 % (3494112)Instructions burned: 27 (million)
% 6.55/1.95 % (3494113)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=1173603845:avsq=on:i=35:doe=on:thsqd=64:nm=64:fsr=off:thsqc=32:rtra=on:tac=light:ss=included:thsq=on:ev=off:sgt=32_2994 on theBenchmark for (2994ds/35Mi)
% 8.31/2.10 % (3494113)Instruction limit reached!
% 8.31/2.10 % (3494113)------------------------------
% 8.31/2.10 % (3494113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494113)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494113)Termination reason: Instruction limit
% 8.31/2.10 % (3494113)Termination phase: Preprocessing 3
% 8.31/2.10 % (3494113)Time elapsed: 0.021 s
% 8.31/2.10 % (3494113)Peak memory usage: 87 MB
% 8.31/2.10 % (3494113)Instructions burned: 36 (million)
% 8.31/2.10 % (3494115)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=4279054449:i=2:fsr=off:rtra=on:inst=on_2994 on theBenchmark for (2994ds/2Mi)
% 8.31/2.10 % (3494115)Instruction limit reached!
% 8.31/2.10 % (3494115)------------------------------
% 8.31/2.10 % (3494115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494115)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494115)Termination reason: Instruction limit
% 8.31/2.10 % (3494115)Termination phase: shuffling
% 8.31/2.10 % (3494115)Time elapsed: 0.002 s
% 8.31/2.10 % (3494115)Peak memory usage: 85 MB
% 8.31/2.10 % (3494115)Instructions burned: 2 (million)
% 8.31/2.10 % (3494120)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=1990479273:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2993 on theBenchmark for (2993ds/13Mi)
% 8.31/2.10 % (3494120)Instruction limit reached!
% 8.31/2.10 % (3494120)------------------------------
% 8.31/2.10 % (3494120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494120)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494120)Termination reason: Instruction limit
% 8.31/2.10 % (3494120)Termination phase: Property scanning
% 8.31/2.10 % (3494120)Time elapsed: 0.004 s
% 8.31/2.10 % (3494120)Peak memory usage: 85 MB
% 8.31/2.10 % (3494120)Instructions burned: 17 (million)
% 8.31/2.10 % (3494108)Instruction limit reached!
% 8.31/2.10 % (3494108)------------------------------
% 8.31/2.10 % (3494108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494108)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494108)Termination reason: Instruction limit
% 8.31/2.10 % (3494108)Termination phase: Saturation
% 8.31/2.10 % (3494108)Time elapsed: 0.101 s
% 8.31/2.10 % (3494108)Peak memory usage: 118 MB
% 8.31/2.10 % (3494108)Instructions burned: 127 (million)
% 8.31/2.10 % (3494119)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=2011559240:i=370:ep=RS:fsr=off:rtra=on_2993 on theBenchmark for (2993ds/370Mi)
% 8.31/2.10 % (3494118)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=3939726091:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2993 on theBenchmark for (2993ds/8Mi)
% 8.31/2.10 % (3494118)Instruction limit reached!
% 8.31/2.10 % (3494118)------------------------------
% 8.31/2.10 % (3494118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494118)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494118)Termination reason: Instruction limit
% 8.31/2.10 % (3494118)Termination phase: Property scanning
% 8.31/2.10 % (3494118)Time elapsed: 0.005 s
% 8.31/2.10 % (3494118)Peak memory usage: 85 MB
% 8.31/2.10 % (3494118)Instructions burned: 9 (million)
% 8.31/2.10 % (3494124)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=196205820:i=226:rtra=on:gtg=position:ss=axioms_2993 on theBenchmark for (2993ds/226Mi)
% 8.31/2.10 % (3494129)lrs+1010_1_to=lpo:prlc=on:sil=128000:prc=on:drc=off:si=on:sp=const_max:thsqr=8,1:tha=some:nwc=5:random_seed=2739544319:i=75:doe=on:thsqd=64:canc=force:thsqc=64:rtra=on:thsq=on_2992 on theBenchmark for (2992ds/75Mi)
% 8.31/2.10 % (3494126)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=324460763:i=10:rtra=on_2992 on theBenchmark for (2992ds/10Mi)
% 8.31/2.10 % (3494126)Instruction limit reached!
% 8.31/2.10 % (3494126)------------------------------
% 8.31/2.10 % (3494126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494126)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494126)Termination reason: Instruction limit
% 8.31/2.10 % (3494126)Termination phase: Property scanning
% 8.31/2.10 % (3494126)Time elapsed: 0.006 s
% 8.31/2.10 % (3494126)Peak memory usage: 86 MB
% 8.31/2.10 % (3494126)Instructions burned: 12 (million)
% 8.31/2.10 % (3494129)Instruction limit reached!
% 8.31/2.10 % (3494129)------------------------------
% 8.31/2.10 % (3494129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494129)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494129)Termination reason: Instruction limit
% 8.31/2.10 % (3494129)Termination phase: Saturation
% 8.31/2.10 % (3494129)Time elapsed: 0.021 s
% 8.31/2.10 % (3494129)Peak memory usage: 90 MB
% 8.31/2.10 % (3494129)Instructions burned: 79 (million)
% 8.31/2.10 % (3494127)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=783729177:i=71:rtra=on:gtg=exists_top_2992 on theBenchmark for (2992ds/71Mi)
% 8.31/2.10 % (3494127)Instruction limit reached!
% 8.31/2.10 % (3494127)------------------------------
% 8.31/2.10 % (3494127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494127)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494127)Termination reason: Instruction limit
% 8.31/2.10 % (3494127)Termination phase: Property scanning
% 8.31/2.10 % (3494127)Time elapsed: 0.037 s
% 8.31/2.10 % (3494127)Peak memory usage: 88 MB
% 8.31/2.10 % (3494127)Instructions burned: 72 (million)
% 8.31/2.10 % (3494130)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=345109854:i=294:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2992 on theBenchmark for (2992ds/294Mi)
% 8.31/2.10 % (3494133)ott+21_1_to=kbo:tgt=full:sas=z3:si=on:tha=off:random_seed=1724112840:i=130:kws=inv_frequency:nm=0:rtra=on:gtg=exists_all_2992 on theBenchmark for (2992ds/130Mi)
% 8.31/2.10 % (3494124)First to succeed.
% 8.31/2.10 % (3494124)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3494065"
% 8.31/2.10 % (3494119)Instruction limit reached!
% 8.31/2.10 % (3494119)------------------------------
% 8.31/2.10 % (3494119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494119)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494119)Termination reason: Instruction limit
% 8.31/2.10 % (3494119)Termination phase: Saturation
% 8.31/2.10 % (3494119)Time elapsed: 0.190 s
% 8.31/2.10 % (3494119)Peak memory usage: 95 MB
% 8.31/2.10 % (3494119)Instructions burned: 370 (million)
% 8.31/2.10 % (3494139)dis+1010_16_to=lpo:sil=64000:thi=strong:sas=z3:si=on:nwc=5:random_seed=103824943:i=40:gtgl=2:rtra=on:gtg=exists_sym:ev=force_2991 on theBenchmark for (2991ds/40Mi)
% 8.31/2.10 % (3494139)Instruction limit reached!
% 8.31/2.10 % (3494139)------------------------------
% 8.31/2.10 % (3494139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494139)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494139)Termination reason: Instruction limit
% 8.31/2.10 % (3494139)Termination phase: Preprocessing 1
% 8.31/2.10 % (3494139)Time elapsed: 0.010 s
% 8.31/2.10 % (3494139)Peak memory usage: 86 MB
% 8.31/2.10 % (3494139)Instructions burned: 44 (million)
% 8.31/2.10 % (3494133)Instruction limit reached!
% 8.31/2.10 % (3494133)------------------------------
% 8.31/2.10 % (3494133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494133)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494133)Termination reason: Instruction limit
% 8.31/2.10 % (3494133)Termination phase: Saturation
% 8.31/2.10 % (3494133)Time elapsed: 0.090 s
% 8.31/2.10 % (3494133)Peak memory usage: 114 MB
% 8.31/2.10 % (3494133)Instructions burned: 131 (million)
% 8.31/2.10 % (3494137)lrs+21_1_to=kbo:sil=64000:thi=all:sas=z3:si=on:spb=goal_then_units:tha=off:nwc=3:random_seed=1306102993:i=131:rtra=on_2991 on theBenchmark for (2991ds/131Mi)
% 8.31/2.10 % (3494140)lrs+10_1_to=lpo:sil=64000:si=on:sos=on:urr=on:random_seed=2881500273:i=307:rtra=on:gtg=exists_top_2990 on theBenchmark for (2990ds/307Mi)
% 8.31/2.10 % (3494145)lrs+1011_5:1_to=kbo:sil=64000:thi=all:si=on:uwa=ground:br=off:random_seed=4143090180:i=131:canc=cautious:fsr=off:rtra=on_2989 on theBenchmark for (2989ds/131Mi)
% 8.31/2.10 % (3494143)ott+1010_3:1_to=kbo:sil=128000:thi=overlap:sas=z3:si=on:urr=on:tha=off:s2agt=32:random_seed=3877039140:s2a=on:i=598:doe=on:bs=on:canc=cautious:fsr=off:rtra=on_2990 on theBenchmark for (2990ds/598Mi)
% 8.31/2.10 % (3494130)Instruction limit reached!
% 8.31/2.10 % (3494130)------------------------------
% 8.31/2.10 % (3494130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494130)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494130)Termination reason: Instruction limit
% 8.31/2.10 % (3494130)Termination phase: Saturation
% 8.31/2.10 % (3494130)Time elapsed: 0.191 s
% 8.31/2.10 % (3494130)Peak memory usage: 93 MB
% 8.31/2.10 % (3494130)Instructions burned: 294 (million)
% 8.31/2.10 % (3494137)Instruction limit reached!
% 8.31/2.10 % (3494137)------------------------------
% 8.31/2.10 % (3494137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494137)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494137)Termination reason: Instruction limit
% 8.31/2.10 % (3494137)Termination phase: Saturation
% 8.31/2.10 % (3494137)Time elapsed: 0.120 s
% 8.31/2.10 % (3494137)Peak memory usage: 135 MB
% 8.31/2.10 % (3494137)Instructions burned: 131 (million)
% 8.31/2.10 % (3494145)Instruction limit reached!
% 8.31/2.10 % (3494145)------------------------------
% 8.31/2.10 % (3494145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.10 % (3494145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.10 % (3494145)CaDiCaL version: 2.1.3
% 8.31/2.10 % (3494145)Termination reason: Instruction limit
% 8.31/2.10 % (3494145)Termination phase: Saturation
% 8.31/2.10 % (3494145)Time elapsed: 0.053 s
% 8.31/2.10 % (3494145)Peak memory usage: 119 MB
% 8.31/2.10 % (3494145)Instructions burned: 134 (million)
% 8.31/2.10 % (3494147)dis+11_1_to=lpo:pum=on:sas=z3:si=on:sp=reverse_arity:sos=theory:thsqr=2,1:tha=some:s2agt=20:random_seed=1998766109:s2pl=no:i=259:sd=10:thsqd=64:thsqc=64:rtra=on:ss=axioms:thsq=on_2989 on theBenchmark for (2989ds/259Mi)
% 8.31/2.10 % (3494124)Refutation found. Thanks to Tanya!
% 8.31/2.10 % SZS status Theorem for theBenchmark
% 8.31/2.10 % SZS output start Proof for theBenchmark
% See solution above
% 8.94/2.30 % (3494124)------------------------------
% 8.94/2.30 % (3494124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.94/2.30 % (3494124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.94/2.30 % (3494124)CaDiCaL version: 2.1.3
% 8.94/2.30 % (3494124)Termination reason: Refutation
% 8.94/2.30 % (3494124)Time elapsed: 0.112 s
% 8.94/2.30 % (3494124)Peak memory usage: 118 MB
% 8.94/2.30 % (3494124)Instructions burned: 156 (million)
% 8.94/2.30 % (3494124)------------------------------
% 8.94/2.30 % (3494124)------------------------------
% 8.94/2.30 % (3494065)Success in time 1.225 s
% 8.94/2.30 % Vampire exiting
%------------------------------------------------------------------------------