%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW473^1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 : Wed Sep 30 08:40:18 AM UTC 2026
% Result : Theorem 0.75s 0.48s
% Output : Refutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 292 ( 50 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 326 ( 41 ~; 33 |; 7 &; 235 @)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 137 ( 134 usr; 8 con; 0-4 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
x_a: $tType ).
thf(type_def_6,type,
pname: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
finite_card_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > nat ).
thf(func_def_1,type,
finite221134632me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > nat ).
thf(func_def_2,type,
finite_card_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > nat ).
thf(func_def_3,type,
finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
thf(func_def_4,type,
finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
thf(func_def_5,type,
finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
thf(func_def_6,type,
finite_card_a: ( x_a > $o ) > nat ).
thf(func_def_7,type,
finite_card_pname: ( pname > $o ) > nat ).
thf(func_def_8,type,
finite_card_nat: ( nat > $o ) > nat ).
thf(func_def_9,type,
finite1302365357_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > $o ).
thf(func_def_10,type,
finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
thf(func_def_11,type,
finite1237261006_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > $o ).
thf(func_def_12,type,
finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(func_def_13,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_14,type,
finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(func_def_15,type,
finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_16,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(func_def_17,type,
finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
thf(func_def_18,type,
finite_finite_a: ( x_a > $o ) > $o ).
thf(func_def_19,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(func_def_20,type,
finite_finite_nat: ( nat > $o ) > $o ).
thf(func_def_21,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_22,type,
suc: nat > nat ).
thf(func_def_23,type,
ord_less_eq_a_o_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(func_def_24,type,
ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_25,type,
ord_le124054423_o_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(func_def_26,type,
ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_27,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_28,type,
ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_29,type,
ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(func_def_30,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_31,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_32,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_33,type,
collect_a_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
thf(func_def_34,type,
collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_35,type,
collect_nat_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $o ).
thf(func_def_36,type,
collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_37,type,
collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_38,type,
collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_39,type,
collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(func_def_40,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_41,type,
collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_42,type,
collect_a: ( x_a > $o ) > x_a > $o ).
thf(func_def_43,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(func_def_44,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(func_def_45,type,
image_a_o_o_a: ( ( ( x_a > $o ) > $o ) > x_a ) > ( ( ( x_a > $o ) > $o ) > $o ) > x_a > $o ).
thf(func_def_46,type,
image_a_o_o_pname: ( ( ( x_a > $o ) > $o ) > pname ) > ( ( ( x_a > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_47,type,
image_a_o_o_nat: ( ( ( x_a > $o ) > $o ) > nat ) > ( ( ( x_a > $o ) > $o ) > $o ) > nat > $o ).
thf(func_def_48,type,
image_pname_o_o_a: ( ( ( pname > $o ) > $o ) > x_a ) > ( ( ( pname > $o ) > $o ) > $o ) > x_a > $o ).
thf(func_def_49,type,
image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_50,type,
image_pname_o_o_nat: ( ( ( pname > $o ) > $o ) > nat ) > ( ( ( pname > $o ) > $o ) > $o ) > nat > $o ).
thf(func_def_51,type,
image_nat_o_o_a: ( ( ( nat > $o ) > $o ) > x_a ) > ( ( ( nat > $o ) > $o ) > $o ) > x_a > $o ).
thf(func_def_52,type,
image_nat_o_o_pname: ( ( ( nat > $o ) > $o ) > pname ) > ( ( ( nat > $o ) > $o ) > $o ) > pname > $o ).
thf(func_def_53,type,
image_nat_o_o_nat: ( ( ( nat > $o ) > $o ) > nat ) > ( ( ( nat > $o ) > $o ) > $o ) > nat > $o ).
thf(func_def_54,type,
image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
thf(func_def_55,type,
image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
thf(func_def_56,type,
image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
thf(func_def_57,type,
image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
thf(func_def_58,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_59,type,
image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
thf(func_def_60,type,
image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
thf(func_def_61,type,
image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
thf(func_def_62,type,
image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
thf(func_def_63,type,
image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
thf(func_def_64,type,
image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
thf(func_def_65,type,
image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
thf(func_def_66,type,
image_pname_a_o_o: ( pname > ( x_a > $o ) > $o ) > ( pname > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_67,type,
image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_68,type,
image_pname_nat_o_o: ( pname > ( nat > $o ) > $o ) > ( pname > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_69,type,
image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
thf(func_def_70,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_71,type,
image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
thf(func_def_72,type,
image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
thf(func_def_73,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(func_def_74,type,
image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
thf(func_def_75,type,
image_nat_a_o_o: ( nat > ( x_a > $o ) > $o ) > ( nat > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_76,type,
image_nat_pname_o_o: ( nat > ( pname > $o ) > $o ) > ( nat > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_77,type,
image_nat_nat_o_o: ( nat > ( nat > $o ) > $o ) > ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_78,type,
image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
thf(func_def_79,type,
image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
thf(func_def_80,type,
image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_81,type,
image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
thf(func_def_82,type,
image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
thf(func_def_83,type,
insert_a_o_o: ( ( x_a > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_84,type,
insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_85,type,
insert_nat_o_o: ( ( nat > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_86,type,
insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
thf(func_def_87,type,
insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_88,type,
insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(func_def_89,type,
insert_a: x_a > ( x_a > $o ) > x_a > $o ).
thf(func_def_90,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(func_def_91,type,
insert_nat: nat > ( nat > $o ) > nat > $o ).
thf(func_def_92,type,
member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
thf(func_def_93,type,
member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_94,type,
member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
thf(func_def_95,type,
member_a: x_a > ( x_a > $o ) > $o ).
thf(func_def_96,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(func_def_97,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(func_def_98,type,
g: x_a > $o ).
thf(func_def_99,type,
p: ( x_a > $o ) > ( x_a > $o ) > $o ).
thf(func_def_100,type,
u: pname > $o ).
thf(func_def_101,type,
mgt_call: pname > x_a ).
thf(func_def_102,type,
na: nat ).
thf(func_def_103,type,
pn: pname ).
thf(func_def_105,type,
vAND: $o > $o > $o ).
thf(func_def_106,type,
vOR: $o > $o > $o ).
thf(func_def_107,type,
vIMP: $o > $o > $o ).
thf(func_def_108,type,
vNOT: $o > $o ).
thf(func_def_111,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_112,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_113,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_114,type,
sK0: ( pname > x_a ) > ( pname > $o ) > pname ).
thf(func_def_115,type,
sK1: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_116,type,
sK2: ( x_a > $o ) > ( x_a > $o ) > x_a ).
thf(func_def_117,type,
sK3: ( nat > pname > $o ) > nat ).
thf(func_def_118,type,
sK4: ( nat > $o ) > nat ).
thf(func_def_119,type,
sK5: nat > ( nat > $o ) > nat ).
thf(func_def_120,type,
sK6: ( nat > $o ) > nat ).
thf(func_def_121,type,
sK7: ( pname > $o ) > ( pname > x_a ) > ( x_a > $o ) > pname > $o ).
thf(func_def_122,type,
sK8: ( nat > x_a > $o ) > nat ).
thf(func_def_123,type,
sK9: ( pname > $o ) > ( pname > x_a ) > ( x_a > $o ) > pname ).
thf(func_def_124,type,
sK10: nat > nat ).
thf(func_def_125,type,
sK11: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_126,type,
sK12: x_a > ( pname > $o ) > ( pname > x_a ) > pname ).
thf(func_def_127,type,
sK13: ( pname > $o ) > ( pname > x_a ) > x_a > pname ).
thf(func_def_128,type,
sK14: ( nat > nat > $o ) > nat ).
thf(func_def_129,type,
sK15: ( nat > nat ) > nat ).
thf(func_def_130,type,
sK16: ( x_a > $o ) > ( pname > $o ) > ( pname > x_a ) > pname > $o ).
thf(func_def_132,type,
inv_suc_18: nat > nat ).
thf(f262,axiom,
! [X2: pname > $o,X0: pname > x_a,X1: pname] :
( ( member_pname @ X1 @ X2 )
=> ( member_a @ ( X0 @ X1 ) @ ( image_pname_a @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_imageI) ).
thf(f275,axiom,
! [X1: x_a > $o,X2: x_a > $o,X0: x_a] :
( ( ( ord_less_eq_a_o @ X1 @ X2 )
& ( member_a @ X0 @ X2 ) )
<=> ( ord_less_eq_a_o @ ( insert_a @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_insert__subset) ).
thf(f302,axiom,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(f305,axiom,
member_pname @ pn @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(f307,conjecture,
ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(f308,negated_conjecture,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(negated_conjecture,[status(cth)],[f307]) ).
thf(f317,plain,
~ ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
inference(rectify,[],[f308]) ).
thf(f318,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(fool_elimination,[],[f317]) ).
thf(f405,plain,
! [X0: x_a > $o,X1: x_a > $o,X2: x_a] :
( ( ( ord_less_eq_a_o @ X0 @ X1 )
& ( member_a @ X2 @ X1 ) )
<=> ( ord_less_eq_a_o @ ( insert_a @ X2 @ X0 ) @ X1 ) ),
inference(rectify,[],[f275]) ).
thf(f406,plain,
! [X0: x_a > $o,X1: x_a > $o,X2: x_a] :
( ( $true
= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X0 ) @ X1 ) )
<=> ( ( ( member_a @ X2 @ X1 )
= $true )
& ( ( ord_less_eq_a_o @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f405]) ).
thf(f575,plain,
! [X0: pname > $o,X1: pname > x_a,X2: pname] :
( ( member_pname @ X2 @ X0 )
=> ( member_a @ ( X1 @ X2 ) @ ( image_pname_a @ X1 @ X0 ) ) ),
inference(rectify,[],[f262]) ).
thf(f576,plain,
! [X2: pname,X1: pname > x_a,X0: pname > $o] :
( ( ( member_pname @ X2 @ X0 )
= $true )
=> ( ( member_a @ ( X1 @ X2 ) @ ( image_pname_a @ X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f575]) ).
thf(f645,plain,
member_pname @ pn @ u,
inference(rectify,[],[f305]) ).
thf(f646,plain,
( ( member_pname @ pn @ u )
= $true ),
inference(fool_elimination,[],[f645]) ).
thf(f835,plain,
ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ),
inference(rectify,[],[f302]) ).
thf(f836,plain,
( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
= $true ),
inference(fool_elimination,[],[f835]) ).
thf(f883,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(flattening,[],[f318]) ).
thf(f1197,plain,
! [X2: pname,X0: pname > $o,X1: pname > x_a] :
( ( ( member_a @ ( X1 @ X2 ) @ ( image_pname_a @ X1 @ X0 ) )
= $true )
| ( ( member_pname @ X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f576]) ).
thf(f1333,plain,
! [X0: pname,X1: pname > $o,X2: pname > x_a] :
( ( $true
= ( member_a @ ( X2 @ X0 ) @ ( image_pname_a @ X2 @ X1 ) ) )
| ( ( member_pname @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f1197]) ).
thf(f1353,plain,
! [X0: x_a > $o,X1: x_a > $o,X2: x_a] :
( ( ( $true
= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X0 ) @ X1 ) )
| ( ( member_a @ X2 @ X1 )
!= $true )
| ( ( ord_less_eq_a_o @ X0 @ X1 )
!= $true ) )
& ( ( ( ( member_a @ X2 @ X1 )
= $true )
& ( ( ord_less_eq_a_o @ X0 @ X1 )
= $true ) )
| ( $true
!= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X0 ) @ X1 ) ) ) ),
inference(nnf_transformation,[],[f406]) ).
thf(f1354,plain,
! [X0: x_a > $o,X1: x_a > $o,X2: x_a] :
( ( ( $true
= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X0 ) @ X1 ) )
| ( ( member_a @ X2 @ X1 )
!= $true )
| ( ( ord_less_eq_a_o @ X0 @ X1 )
!= $true ) )
& ( ( ( ( member_a @ X2 @ X1 )
= $true )
& ( ( ord_less_eq_a_o @ X0 @ X1 )
= $true ) )
| ( $true
!= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X0 ) @ X1 ) ) ) ),
inference(flattening,[],[f1353]) ).
thf(f1496,plain,
( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true ),
inference(cnf_transformation,[],[f883]) ).
thf(f1502,plain,
( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
= $true ),
inference(cnf_transformation,[],[f836]) ).
thf(f1642,plain,
! [X2: pname > x_a,X0: pname,X1: pname > $o] :
( ( $true
= ( member_a @ ( X2 @ X0 ) @ ( image_pname_a @ X2 @ X1 ) ) )
| ( ( member_pname @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f1333]) ).
thf(f1690,plain,
! [X2: x_a,X0: x_a > $o,X1: x_a > $o] :
( ( $true
= ( ord_less_eq_a_o @ ( insert_a @ X2 @ X0 ) @ X1 ) )
| ( ( ord_less_eq_a_o @ X0 @ X1 )
!= $true )
| ( ( member_a @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f1354]) ).
thf(f1781,plain,
( ( member_pname @ pn @ u )
= $true ),
inference(cnf_transformation,[],[f646]) ).
thf(f1871,definition,
( spl17_1
<=> ( ( member_pname @ pn @ u )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
thf(f1873,plain,
( ( ( member_pname @ pn @ u )
= $true )
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f1871]) ).
thf(f1874,plain,
spl17_1,
inference(avatar_split_clause,[],[f1781,f1871]) ).
thf(f1886,definition,
( spl17_4
<=> ( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
thf(f1888,plain,
( ( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
= $true )
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f1886]) ).
thf(f1889,plain,
spl17_4,
inference(avatar_split_clause,[],[f1502,f1886]) ).
thf(f1901,definition,
( spl17_7
<=> ( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
thf(f1903,plain,
( ( ( ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) )
!= $true )
| spl17_7 ),
inference(avatar_component_clause,[],[f1901]) ).
thf(f1904,plain,
~ spl17_7,
inference(avatar_split_clause,[],[f1496,f1901]) ).
thf(f2155,plain,
( ( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
!= $true )
| ( $true
!= ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) )
| ( $true != $true )
| spl17_7 ),
inference(superposition,[],[f1903,f1690]) ).
thf(f2161,plain,
( ( ( ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) )
!= $true )
| ( $true
!= ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) )
| spl17_7 ),
inference(trivial_inequality_removal,[],[f2155]) ).
thf(f2169,plain,
( ( $true
!= ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) )
| ~ spl17_4
| spl17_7 ),
inference(forward_subsumption_resolution,[],[f2161,f1888]) ).
thf(f2171,definition,
( spl17_13
<=> ( $true
= ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_13])],[avatar_definition]) ).
thf(f2173,plain,
( ( $true
!= ( member_a @ ( mgt_call @ pn ) @ ( image_pname_a @ mgt_call @ u ) ) )
| spl17_13 ),
inference(avatar_component_clause,[],[f2171]) ).
thf(f2174,plain,
( ~ spl17_13
| ~ spl17_4
| spl17_7 ),
inference(avatar_split_clause,[],[f2169,f1901,f1886,f2171]) ).
thf(f2195,plain,
( ( ( member_pname @ pn @ u )
!= $true )
| ( $true != $true )
| spl17_13 ),
inference(superposition,[],[f2173,f1642]) ).
thf(f2196,plain,
( ( ( member_pname @ pn @ u )
!= $true )
| spl17_13 ),
inference(trivial_inequality_removal,[],[f2195]) ).
thf(f2197,plain,
( $false
| ~ spl17_1
| spl17_13 ),
inference(forward_subsumption_resolution,[],[f2196,f1873]) ).
thf(f2198,plain,
( ~ spl17_1
| spl17_13 ),
inference(avatar_contradiction_clause,[],[f2197]) ).
cnf(s1,plain,
spl17_1,
inference(sat_conversion,[],[f1874]) ).
cnf(s4,plain,
spl17_4,
inference(sat_conversion,[],[f1889]) ).
cnf(s7,plain,
~ spl17_7,
inference(sat_conversion,[],[f1904]) ).
cnf(s12,plain,
( ~ spl17_4
| spl17_7
| ~ spl17_13 ),
inference(sat_conversion,[],[f2174]) ).
cnf(s13,plain,
( ~ spl17_1
| spl17_13 ),
inference(sat_conversion,[],[f2198]) ).
cnf(s16,plain,
~ spl17_13,
inference(rat,[],[s12,s7,s4]) ).
cnf(s18,plain,
~ spl17_1,
inference(rat,[],[s13,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s18]) ).
thf(f2199,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n017.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 16:01:07 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.30 Running higher-order theorem proving
% 0.27/0.35 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.33/0.48 % (513876)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.48 % (513884)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1003828631:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.33/0.48 % (513881)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2254037080:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.48 % (513887)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.48 % (513887)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.33/0.48 % (513885)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=84125500:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.48 % (513882)lrs+10_16_si=on:nwc=1.5:random_seed=645342363:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.48 % (513886)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=234474022:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.48 % (513887)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3456973962:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.48 % (513883)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1347938503:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.48 % (513883)Instruction limit reached!
% 0.33/0.48 % (513883)------------------------------
% 0.33/0.48 % (513883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.48 % (513883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.48 % (513883)CaDiCaL version: 2.1.3
% 0.33/0.48 % (513883)Termination reason: Instruction limit
% 0.75/0.48 % (513883)Termination phase: shuffling
% 0.75/0.48 % (513883)Time elapsed: 0.003 s
% 0.75/0.48 % (513883)Peak memory usage: 10 MB
% 0.75/0.48 % (513883)Instructions burned: 3 (million)
% 0.75/0.48 % (513882)Instruction limit reached!
% 0.75/0.48 % (513882)------------------------------
% 0.75/0.48 % (513882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.48 % (513882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.48 % (513882)CaDiCaL version: 2.1.3
% 0.75/0.48 % (513882)Termination reason: Instruction limit
% 0.75/0.48 % (513882)Termination phase: shuffling
% 0.75/0.48 % (513882)Time elapsed: 0.015 s
% 0.75/0.48 % (513882)Peak memory usage: 10 MB
% 0.75/0.48 % (513882)Instructions burned: 18 (million)
% 0.75/0.48 % (513885)Instruction limit reached!
% 0.75/0.48 % (513885)------------------------------
% 0.75/0.48 % (513885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.48 % (513885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.48 % (513885)CaDiCaL version: 2.1.3
% 0.75/0.48 % (513885)Termination reason: Instruction limit
% 0.75/0.48 % (513885)Termination phase: Property scanning
% 0.75/0.48 % (513885)Time elapsed: 0.020 s
% 0.75/0.48 % (513885)Peak memory usage: 10 MB
% 0.75/0.48 % (513885)Instructions burned: 24 (million)
% 0.75/0.48 % (513895)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3633481865:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.75/0.48 % (513895)Instruction limit reached!
% 0.75/0.48 % (513895)------------------------------
% 0.75/0.48 % (513895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.48 % (513895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.48 % (513895)CaDiCaL version: 2.1.3
% 0.75/0.48 % (513895)Termination reason: Instruction limit
% 0.75/0.48 % (513895)Termination phase: shuffling
% 0.75/0.48 % (513895)Time elapsed: 0.004 s
% 0.75/0.48 % (513895)Peak memory usage: 10 MB
% 0.75/0.48 % (513895)Instructions burned: 4 (million)
% 0.75/0.48 % (513897)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.75/0.48 % (513896)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=924780857:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.75/0.48 % (513884) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-513876-513884"...
% 0.75/0.48 % (513881)Instruction limit reached!
% 0.75/0.48 % (513881)------------------------------
% 0.75/0.48 % (513881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.48 % (513881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.48 % (513881)CaDiCaL version: 2.1.3
% 0.75/0.48 % (513897)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4270762036:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.75/0.48 % (513881)Termination reason: Instruction limit
% 0.75/0.48 % (513881)Termination phase: Saturation
% 0.75/0.48 % (513881)Time elapsed: 0.063 s
% 0.75/0.48 % (513881)Peak memory usage: 12 MB
% 0.75/0.48 % (513881)Instructions burned: 87 (million)
% 0.75/0.48 % (513884)...printing done.
% 0.75/0.48 % (513896)Instruction limit reached!
% 0.75/0.48 % (513896)------------------------------
% 0.75/0.48 % (513896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.48 % (513896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.48 % (513896)CaDiCaL version: 2.1.3
% 0.75/0.48 % (513896)Termination reason: Instruction limit
% 0.75/0.48 % (513896)Termination phase: shuffling
% 0.75/0.48 % (513896)Time elapsed: 0.006 s
% 0.75/0.48 % (513896)Peak memory usage: 10 MB
% 0.75/0.48 % (513896)Instructions burned: 5 (million)
% 0.75/0.48 % (513884)Refutation found. Thanks to Tanya!
% 0.75/0.48 % SZS status Theorem for theBenchmark
% 0.75/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.75/0.49 % (513884)------------------------------
% 0.75/0.49 % (513884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.75/0.49 % (513884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/0.49 % (513884)CaDiCaL version: 2.1.3
% 0.75/0.49 % (513884)Termination reason: Refutation
% 0.75/0.49 % (513884)Time elapsed: 0.067 s
% 0.75/0.49 % (513884)Peak memory usage: 14 MB
% 0.75/0.49 % (513884)Instructions burned: 147 (million)
% 0.75/0.49 % (513876)Success in time 0.118 s
% 0.75/0.49 % Vampire exiting
%------------------------------------------------------------------------------