TSTP Solution File: ITP051^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP051^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:48:58 EDT 2024
% Result : ContradictoryAxioms 2.42s 0.72s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 131
% Syntax : Number of formulae : 175 ( 22 unt; 121 typ; 0 def)
% Number of atoms : 555 ( 88 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 74 ( 25 ~; 31 |; 5 &; 0 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 271 ( 268 >; 3 *; 0 +; 0 <<)
% Number of symbols : 122 ( 119 usr; 8 con; 0-6 aty)
% Number of variables : 138 ( 0 ^ 56 !; 2 ?; 138 :)
% ( 80 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
set: $tType > $tType ).
thf(type_def_9,type,
list: $tType > $tType ).
thf(type_def_10,type,
a: $tType ).
thf(type_def_11,type,
b: $tType ).
thf(func_def_0,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
list: $tType > $tType ).
thf(func_def_2,type,
set: $tType > $tType ).
thf(func_def_3,type,
nat: $tType ).
thf(func_def_4,type,
b: $tType ).
thf(func_def_5,type,
a: $tType ).
thf(func_def_6,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_7,type,
size:
!>[X0: $tType] : $o ).
thf(func_def_8,type,
zero:
!>[X0: $tType] : $o ).
thf(func_def_9,type,
order:
!>[X0: $tType] : $o ).
thf(func_def_10,type,
finite_finite:
!>[X0: $tType] : $o ).
thf(func_def_11,type,
wellorder:
!>[X0: $tType] : $o ).
thf(func_def_12,type,
linordered_idom:
!>[X0: $tType] : $o ).
thf(func_def_13,type,
canoni770627133id_add:
!>[X0: $tType] : $o ).
thf(func_def_14,type,
edmond2129202899alysis:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > $o ) ).
thf(func_def_15,type,
edmond115586663easure:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > nat > nat ) ).
thf(func_def_16,type,
edmond1803015688pEdges:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > nat > set(product_prod(nat,nat)) ) ).
thf(func_def_17,type,
edmond259086305sis_uE:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(product_prod(nat,nat)) ) ).
thf(func_def_18,type,
finite_card:
!>[X0: $tType] : ( set(X0) > nat ) ).
thf(func_def_19,type,
finite_finite2:
!>[X0: $tType] : ( set(X0) > $o ) ).
thf(func_def_20,type,
finite_Graph:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > $o ) ).
thf(func_def_21,type,
e:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(product_prod(nat,nat)) ) ).
thf(func_def_22,type,
v:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(nat) ) ).
thf(func_def_23,type,
adjacent_nodes:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > set(nat) ) ).
thf(func_def_24,type,
connected:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > nat > $o ) ).
thf(func_def_25,type,
dist:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > nat > nat > $o ) ).
thf(func_def_26,type,
incoming:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(nat) > set(product_prod(nat,nat)) ) ).
thf(func_def_27,type,
isPath:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > list(product_prod(nat,nat)) > nat > $o ) ).
thf(func_def_28,type,
isShortestPath:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > list(product_prod(nat,nat)) > nat > $o ) ).
thf(func_def_29,type,
isSimplePath:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > list(product_prod(nat,nat)) > nat > $o ) ).
thf(func_def_30,type,
min_dist:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > nat > nat ) ).
thf(func_def_31,type,
outgoing:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > set(nat) > set(product_prod(nat,nat)) ) ).
thf(func_def_32,type,
reachableNodes:
!>[X0: $tType] : ( ( product_prod(nat,nat) > X0 ) > nat > set(nat) ) ).
thf(func_def_33,type,
zero_zero:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
set2:
!>[X0: $tType] : ( list(X0) > set(X0) ) ).
thf(func_def_35,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
thf(func_def_36,type,
ord_less:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_37,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_39,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_40,type,
c: product_prod(nat,nat) > a ).
thf(func_def_41,type,
c2: product_prod(nat,nat) > b ).
thf(func_def_42,type,
edges: set(product_prod(nat,nat)) ).
thf(func_def_43,type,
p: list(product_prod(nat,nat)) ).
thf(func_def_44,type,
p2: list(product_prod(nat,nat)) ).
thf(func_def_45,type,
s: nat ).
thf(func_def_46,type,
t: nat ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
vNOT: $o > $o ).
thf(func_def_53,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_54,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_55,type,
vOR: $o > $o > $o ).
thf(func_def_56,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_57,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_58,type,
vIMP: $o > $o > $o ).
thf(func_def_59,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_60,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_61,type,
sP0:
!>[X0: $tType] : ( set(X0) > nat > $o ) ).
thf(func_def_62,type,
sP1:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).
thf(func_def_63,type,
sK2: list(product_prod(nat,nat)) ).
thf(func_def_64,type,
sK3:
!>[X0: $tType] : ( X0 > set(X0) > X0 ) ).
thf(func_def_65,type,
sK4:
!>[X0: $tType] : ( X0 > set(X0) > X0 ) ).
thf(func_def_66,type,
sK5:
!>[X0: $tType] : ( nat > nat > ( product_prod(nat,nat) > X0 ) > list(product_prod(nat,nat)) ) ).
thf(func_def_67,type,
sK6:
!>[X0: $tType] : ( ( nat > $o ) > nat > nat > ( product_prod(nat,nat) > X0 ) > nat ) ).
thf(func_def_68,type,
sK7:
!>[X0: $tType] : ( nat > nat > ( product_prod(nat,nat) > X0 ) > nat ) ).
thf(func_def_69,type,
sK8:
!>[X0: $tType] : ( nat > nat > nat > ( product_prod(nat,nat) > X0 ) > nat ) ).
thf(func_def_70,type,
sK9:
!>[X0: $tType] : ( nat > nat > ( product_prod(nat,nat) > X0 ) > list(product_prod(nat,nat)) ) ).
thf(func_def_71,type,
sK10:
!>[X0: $tType] : ( nat > nat > ( product_prod(nat,nat) > X0 ) > nat ) ).
thf(func_def_72,type,
sK11: ( nat > $o ) > nat ).
thf(func_def_73,type,
sK12: ( nat > $o ) > nat ).
thf(func_def_74,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_75,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_76,type,
sK15: nat > ( nat > $o ) > nat ).
thf(func_def_77,type,
sK16: ( nat > $o ) > nat ).
thf(func_def_78,type,
sK17:
!>[X0: $tType] : ( set(list(X0)) > nat ) ).
thf(func_def_79,type,
sK18: nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_80,type,
sK19: nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_81,type,
sK20:
!>[X0: $tType] : ( nat > list(X0) ) ).
thf(func_def_82,type,
sK21:
!>[X0: $tType] : ( nat > set(X0) > set(X0) ) ).
thf(func_def_83,type,
sK22:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_84,type,
sK23:
!>[X0: $tType] : ( ( list(X0) > $o ) > list(X0) ) ).
thf(func_def_85,type,
sK24:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_86,type,
sK25:
!>[X0: $tType] : ( set(X0) > nat > set(X0) ) ).
thf(func_def_87,type,
sK26: ( nat > nat ) > nat ).
thf(func_def_88,type,
sK27: ( nat > nat ) > nat ).
thf(func_def_89,type,
sK28: ( nat > $o ) > nat ).
thf(func_def_90,type,
sK29: nat > ( nat > $o ) > nat ).
thf(func_def_91,type,
sK30:
!>[X0: $tType] : ( ( set(X0) > $o ) > set(X0) ) ).
thf(func_def_92,type,
sK31: ( nat > $o ) > nat > nat > nat ).
thf(func_def_93,type,
sK32: nat > nat > nat ).
thf(func_def_94,type,
sK33: ( nat > $o ) > nat > nat > nat ).
thf(func_def_95,type,
sK34: nat > nat > nat ).
thf(func_def_96,type,
sK35: nat > nat > nat > nat ).
thf(func_def_97,type,
sK36: nat > nat > nat > nat ).
thf(func_def_98,type,
sK37: nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_99,type,
sK38: nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_100,type,
sK39:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_101,type,
sK40:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_102,type,
sK41:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_103,type,
sK42:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_104,type,
sK43:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > set(X1) > X1 > X0 ) ).
thf(func_def_105,type,
sK44:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 > $o ) > set(X1) > X1 ) ).
thf(func_def_106,type,
sK45: nat > nat > nat ).
thf(func_def_107,type,
sK46: nat > nat > nat ).
thf(func_def_109,type,
sK48: list(product_prod(nat,nat)) > nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_110,type,
sK49: list(product_prod(nat,nat)) > nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_111,type,
sK50: nat > nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_112,type,
sK51: nat > nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_113,type,
sK52:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_114,type,
sK53: nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_115,type,
sK54: nat > nat > nat ).
thf(func_def_116,type,
sK55: nat > nat > list(product_prod(nat,nat)) ).
thf(func_def_117,type,
sK56: nat > nat > nat ).
thf(f8806,plain,
$false,
inference(trivial_inequality_removal,[],[f8805]) ).
thf(f8805,plain,
$true = $false,
inference(backward_demodulation,[],[f1730,f8804]) ).
thf(f8804,plain,
$false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),
inference(trivial_inequality_removal,[],[f8789]) ).
thf(f8789,plain,
( ( $true = $false )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)) ) ),
inference(superposition,[],[f1726,f4405]) ).
thf(f4405,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(trivial_inequality_removal,[],[f4385]) ).
thf(f4385,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(superposition,[],[f2740,f2377]) ).
thf(f2377,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(trivial_inequality_removal,[],[f2376]) ).
thf(f2376,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(superposition,[],[f1311,f277]) ).
thf(f277,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1311,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(cnf_transformation,[],[f943]) ).
thf(f943,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( ( X0 != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ) ),
inference(ennf_transformation,[],[f567]) ).
thf(f567,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(fool_elimination,[],[f566]) ).
thf(f566,plain,
! [X0: nat,X1: nat] :
( ( ( X0 = X1 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ),
inference(rectify,[],[f92]) ).
thf(f92,axiom,
! [X42: nat,X30: nat] :
( ( ( X30 = X42 )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X42),X30) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X42),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__or__eq__imp__le) ).
thf(f2740,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(subsumption_resolution,[],[f2738,f1592]) ).
thf(f1592,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) ) ),
inference(binary_proxy_clausification,[],[f1591]) ).
thf(f1591,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ) ),
inference(equality_proxy_clausification,[],[f1590]) ).
thf(f1590,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ) ),
inference(not_proxy_clausification,[],[f1585]) ).
thf(f1585,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1298]) ).
thf(f1298,plain,
! [X0: nat,X1: nat] : ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ),
inference(cnf_transformation,[],[f541]) ).
thf(f541,plain,
! [X0: nat,X1: nat] : ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) ),
inference(fool_elimination,[],[f540]) ).
thf(f540,plain,
! [X0: nat,X1: nat] :
( ( ( X0 != X1 )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ),
inference(rectify,[],[f104]) ).
thf(f104,axiom,
! [X42: nat,X30: nat] :
( ( ( X30 != X42 )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X30),X42) )
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X42),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_nat__neq__iff) ).
thf(f2738,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( X0 = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(trivial_inequality_removal,[],[f2718]) ).
thf(f2718,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( X0 = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(superposition,[],[f1335,f2377]) ).
thf(f1335,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f962]) ).
thf(f962,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(flattening,[],[f961]) ).
thf(f961,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(ennf_transformation,[],[f597]) ).
thf(f597,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f596]) ).
thf(f596,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
! [X42: nat,X30: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X42),X30)
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X30),X42)
=> ( X30 = X42 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_le__antisym) ).
thf(f1726,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2)),
inference(forward_demodulation,[],[f1458,f1685]) ).
thf(f1685,plain,
vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2),
inference(backward_demodulation,[],[f1155,f1167]) ).
thf(f1167,plain,
vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2),
inference(cnf_transformation,[],[f1060]) ).
thf(f1060,plain,
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2) )
& ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),sK2),t) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f837,f1059]) ).
thf(f1059,plain,
( ? [X0: list(product_prod(nat,nat))] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X0) )
& ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X0),t) ) )
=> ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2) )
& ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),sK2),t) ) ) ),
introduced(choice_axiom,[]) ).
thf(f837,plain,
? [X0: list(product_prod(nat,nat))] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) = vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X0) )
& ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X0),t) ) ),
inference(ennf_transformation,[],[f301]) ).
thf(f301,plain,
~ ! [X0: list(product_prod(nat,nat))] :
( ( $true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X0),t) )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) != vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X0) ) ),
inference(fool_elimination,[],[f300]) ).
thf(f300,plain,
~ ! [X0: list(product_prod(nat,nat))] :
( vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X0),t)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) != vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X0) ) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
~ ! [X4: list(product_prod(nat,nat))] :
( vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(b),c2),s),X4),t)
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t) != vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062p_H_O_A_092_060lbrakk_062g_H_OisPath_As_Ap_H_At_059_Alength_Ap_H_A_061_Ag_H_Omin__dist_As_At_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(f1155,plain,
vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t),
inference(cnf_transformation,[],[f3]) ).
thf(f3,axiom,
vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_LENP_H) ).
thf(f1458,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)) = $true,
inference(cnf_transformation,[],[f773]) ).
thf(f773,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)) = $true,
inference(fool_elimination,[],[f772]) ).
thf(f772,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062) ).
thf(f1730,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),sK2)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),
inference(forward_demodulation,[],[f1729,f1167]) ).
thf(f1729,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p)),
inference(forward_demodulation,[],[f1468,f1156]) ).
thf(f1156,plain,
vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t),
inference(cnf_transformation,[],[f2]) ).
thf(f2,axiom,
vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_LENP) ).
thf(f1468,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t)) = $true,
inference(cnf_transformation,[],[f793]) ).
thf(f793,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t)) = $true,
inference(fool_elimination,[],[f792]) ).
thf(f792,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t)),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),b),sTfun(nat,sTfun(nat,nat)),min_dist(b),c2),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c),s),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_SHORTER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP051^2 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 18:25:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (6444)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (6447)WARNING: value z3 for option sas not known
% 0.14/0.39 % (6448)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (6445)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (6446)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (6449)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.39 % (6447)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39 % (6450)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39 % (6451)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.42 % (6451)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.43 % Exception at run slice level
% 0.20/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.43 % Exception at run slice level
% 0.20/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.43 % Exception at run slice level
% 0.20/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.44 % (6452)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.44 % (6453)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.44 % (6454)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.47 % (6452)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.47 % (6453)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.48 % Exception at run slice level
% 0.20/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.49 % (6455)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 2.42/0.72 % (6454)First to succeed.
% 2.42/0.72 % (6454)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6444"
% 2.42/0.72 % (6454)Refutation found. Thanks to Tanya!
% 2.42/0.72 % SZS status ContradictoryAxioms for theBenchmark
% 2.42/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.42/0.72 % (6454)------------------------------
% 2.42/0.72 % (6454)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.42/0.72 % (6454)Termination reason: Refutation
% 2.42/0.72
% 2.42/0.72 % (6454)Memory used [KB]: 3354
% 2.42/0.72 % (6454)Time elapsed: 0.280 s
% 2.42/0.72 % (6454)Instructions burned: 866 (million)
% 2.42/0.72 % (6444)Success in time 0.347 s
%------------------------------------------------------------------------------