%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM705^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:18:38 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 557 ( 135 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 745 ( 181 ~; 94 |; 16 &; 334 @)
% ( 6 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 11 con; 0-4 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 121 ( 0 sgn 74 !; 6 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
p: nat > $o ).
thf(func_def_1,type,
some: ( nat > $o ) > $o ).
thf(func_def_3,type,
lessis: nat > nat > $o ).
thf(func_def_4,type,
more: nat > nat > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
sK0: nat ).
thf(func_def_14,type,
sK1: nat ).
thf(f1,axiom,
some @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( lessis @ X0 @ X1 )
=> ( ~ ( more @ X1 @ X0 )
=> ( X1 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz14) ).
thf(f4,axiom,
! [X1: nat,X0: nat] :
( ( lessis @ X0 @ X1 )
=> ~ ( more @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10d) ).
thf(f5,axiom,
! [X0: nat > $o] :
( ( some @ X0 )
=> ( some
@ ^ [X1: nat] :
~ ( ! [X2: nat] :
( ( X0 @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz27) ).
thf(f6,conjecture,
~ ( ! [X0: nat,X1: nat] :
( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X0 @ X2 ) )
=> ~ ( p @ X0 ) )
=> ( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) )
=> ( X0 = X1 ) ) )
=> ~ ( some
@ ^ [X0: nat] :
~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X0 @ X2 ) )
=> ~ ( p @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz27a) ).
thf(f7,negated_conjecture,
~ ~ ( ! [X0: nat,X1: nat] :
( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X0 @ X2 ) )
=> ~ ( p @ X0 ) )
=> ( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) )
=> ( X0 = X1 ) ) )
=> ~ ( some
@ ^ [X0: nat] :
~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X0 @ X2 ) )
=> ~ ( p @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X1 @ X0 )
=> ~ ( more @ X1 @ X0 ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X1 @ X0 ) )
=> ( ( more @ X1 @ X0 )
!= $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f12,plain,
some @ p,
inference(rectify,[],[f1]) ).
thf(f13,plain,
( ( some @ p )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X1 @ X0 )
=> ( ~ ( more @ X0 @ X1 )
=> ( X1 = X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X1 @ X0 ) )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
~ ~ ( ! [X0: nat,X1: nat] :
( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X0 @ X2 ) )
=> ~ ( p @ X0 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X1 @ X3 ) )
=> ~ ( p @ X1 ) )
=> ( X0 = X1 ) ) )
=> ~ ( some
@ ^ [X4: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X4 @ X5 ) )
=> ~ ( p @ X4 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f17,plain,
~ ~ ( ! [X0: nat,X1: nat] :
( ~ ( ! [X2: nat] :
( ( ( p @ X2 )
= $true )
=> ( ( lessis @ X0 @ X2 )
= $true ) )
=> ( ( p @ X0 )
!= $true ) )
=> ( ~ ( ! [X3: nat] :
( ( ( p @ X3 )
= $true )
=> ( $true
= ( lessis @ X1 @ X3 ) ) )
=> ( ( p @ X1 )
!= $true ) )
=> ( X0 = X1 ) ) )
=> ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: nat > $o] :
( ( some @ X0 )
=> ( some
@ ^ [X1: nat] :
~ ( ! [X2: nat] :
( ( X0 @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f19,plain,
! [X0: nat > $o] :
( ( ( some @ X0 )
= $true )
=> ( $true
= ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( X0 @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X1 @ X0 ) )
=> ( ( more @ X1 @ X0 )
!= $true ) ),
inference(flattening,[],[f9]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X1 @ X0 ) )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( X0 = X1 ) ) ),
inference(flattening,[],[f15]) ).
thf(f23,plain,
( ! [X1: nat,X0: nat] :
( ~ ( ! [X2: nat] :
( ( ( p @ X2 )
= $true )
=> ( ( lessis @ X0 @ X2 )
= $true ) )
=> ( ( p @ X0 )
!= $true ) )
=> ( ~ ( ! [X3: nat] :
( ( ( p @ X3 )
= $true )
=> ( $true
= ( lessis @ X1 @ X3 ) ) )
=> ( ( p @ X1 )
!= $true ) )
=> ( X0 = X1 ) ) )
=> ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(flattening,[],[f17]) ).
thf(f24,plain,
! [X0: nat > $o] :
( ( ( some @ X0 )
!= $true )
| ( $true
= ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( X0 @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f25,plain,
! [X1: nat,X0: nat] :
( ( ( more @ X1 @ X0 )
!= $true )
| ( $true
!= ( lessis @ X1 @ X0 ) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f27,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ( more @ X0 @ X1 )
= $true )
| ( $true
!= ( lessis @ X1 @ X0 ) ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f28,plain,
! [X1: nat,X0: nat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( $true
!= ( lessis @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(flattening,[],[f27]) ).
thf(f29,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ? [X1: nat,X0: nat] :
( ( X0 != X1 )
& ( ( p @ X1 )
= $true )
& ! [X3: nat] :
( ( ( p @ X3 )
!= $true )
| ( $true
= ( lessis @ X1 @ X3 ) ) )
& ( ( p @ X0 )
= $true )
& ! [X2: nat] :
( ( ( lessis @ X0 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true ) ) ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f30,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ? [X1: nat,X0: nat] :
( ( ( p @ X0 )
= $true )
& ! [X2: nat] :
( ( ( lessis @ X0 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true ) )
& ( ( p @ X1 )
= $true )
& ! [X3: nat] :
( ( ( p @ X3 )
!= $true )
| ( $true
= ( lessis @ X1 @ X3 ) ) )
& ( X0 != X1 ) ) ),
inference(flattening,[],[f29]) ).
thf(f31,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true )
| ( X0 = X1 ) ),
inference(rectify,[],[f28]) ).
thf(f32,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f25]) ).
thf(f33,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ? [X0: nat,X1: nat] :
( ( ( p @ X1 )
= $true )
& ! [X2: nat] :
( ( ( lessis @ X1 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true ) )
& ( ( p @ X0 )
= $true )
& ! [X3: nat] :
( ( ( p @ X3 )
!= $true )
| ( ( lessis @ X0 @ X3 )
= $true ) )
& ( X0 != X1 ) ) ),
inference(rectify,[],[f30]) ).
thf(f34,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ( ( $true
= ( p @ sK1 ) )
& ! [X2: nat] :
( ( ( lessis @ sK1 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true ) )
& ( ( p @ sK0 )
= $true )
& ! [X3: nat] :
( ( ( p @ X3 )
!= $true )
| ( ( lessis @ sK0 @ X3 )
= $true ) )
& ( sK1 != sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f33]) ).
thf(f35,plain,
( ( some @ p )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f36,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
!= $true )
| ( ( more @ X1 @ X0 )
= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f37,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f38,plain,
! [X0: nat > $o] :
( ( ( some @ X0 )
!= $true )
| ( $true
= ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( X0 @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( X0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f39,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ( sK1 != sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f40,plain,
! [X3: nat] :
( ( ( lessis @ sK0 @ X3 )
= $true )
| ( ( p @ X3 )
!= $true )
| ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f41,plain,
( ( ( p @ sK0 )
= $true )
| ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f42,plain,
! [X2: nat] :
( ( ( lessis @ sK1 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true )
| ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f43,plain,
( ( $true
= ( p @ sK1 ) )
| ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f49,definition,
( spl2_1
<=> ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f51,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| spl2_1 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f53,definition,
( spl2_2
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f55,plain,
( ( sK1 != sK0 )
| spl2_2 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f39,f53,f49]) ).
thf(f58,definition,
( spl2_3
<=> ! [X2: nat] :
( ( ( lessis @ sK1 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f59,plain,
( ! [X2: nat] :
( ( ( p @ X2 )
!= $true )
| ( ( lessis @ sK1 @ X2 )
= $true ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f60,plain,
( spl2_3
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f42,f49,f58]) ).
thf(f62,definition,
( spl2_4
<=> ! [X3: nat] :
( ( ( lessis @ sK0 @ X3 )
= $true )
| ( ( p @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f63,plain,
( ! [X3: nat] :
( ( ( p @ X3 )
!= $true )
| ( ( lessis @ sK0 @ X3 )
= $true ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f64,plain,
( ~ spl2_1
| spl2_4 ),
inference(avatar_split_clause,[],[f40,f62,f49]) ).
thf(f66,definition,
( spl2_5
<=> ( $true
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f68,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f69,plain,
( ~ spl2_1
| spl2_5 ),
inference(avatar_split_clause,[],[f43,f66,f49]) ).
thf(f71,definition,
( spl2_6
<=> ( ( p @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
thf(f73,plain,
( ( ( p @ sK0 )
= $true )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f74,plain,
( spl2_6
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f41,f49,f71]) ).
thf(f75,plain,
( ( $true != $true )
| ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
= $true ) ),
inference(constrained_superposition,[],[f38,f35]) ).
thf(f76,plain,
( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f77,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f76,f51]) ).
thf(f78,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f77]) ).
thf(f80,plain,
( ( $true != $true )
| ( $true
= ( lessis @ sK1 @ sK0 ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(constrained_superposition,[],[f59,f73]) ).
thf(f82,plain,
( ( $true
= ( lessis @ sK1 @ sK0 ) )
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f83,plain,
( ( $true != $true )
| ( ( more @ sK0 @ sK1 )
= $true )
| ( sK1 = sK0 )
| ~ spl2_3
| ~ spl2_6 ),
inference(constrained_superposition,[],[f36,f82]) ).
thf(f84,plain,
( ( sK1 = sK0 )
| ( ( more @ sK0 @ sK1 )
= $true )
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f85,plain,
( ( ( more @ sK0 @ sK1 )
= $true )
| spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f84,f55]) ).
thf(f86,plain,
( ( ( lessis @ sK0 @ sK1 )
!= $true )
| ( $true != $true )
| spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(constrained_superposition,[],[f37,f85]) ).
thf(f87,plain,
( ( ( lessis @ sK0 @ sK1 )
!= $true )
| spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f88,plain,
( ( $true != $true )
| ( ( lessis @ sK0 @ sK1 )
= $true )
| ~ spl2_4
| ~ spl2_5 ),
inference(constrained_superposition,[],[f63,f68]) ).
thf(f91,plain,
( ( ( lessis @ sK0 @ sK1 )
= $true )
| ~ spl2_4
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f88]) ).
thf(f92,plain,
( $false
| spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f91,f87]) ).
thf(f93,plain,
( spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f92]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f60]) ).
cnf(s3,plain,
( ~ spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f64]) ).
cnf(s4,plain,
( ~ spl2_1
| spl2_5 ),
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( ~ spl2_1
| spl2_6 ),
inference(sat_conversion,[],[f74]) ).
cnf(s6,plain,
spl2_1,
inference(sat_conversion,[],[f78]) ).
cnf(s7,plain,
( spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(sat_conversion,[],[f93]) ).
cnf(s8,plain,
spl2_6,
inference(rat,[],[s5,s6]) ).
cnf(s9,plain,
spl2_5,
inference(rat,[],[s4,s6]) ).
cnf(s10,plain,
spl2_4,
inference(rat,[],[s3,s6]) ).
cnf(s11,plain,
spl2_3,
inference(rat,[],[s2,s6]) ).
cnf(s12,plain,
spl2_2,
inference(rat,[],[s7,s8,s9,s10,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s12,s6]) ).
thf(f94,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM705^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:42:16 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.09/0.28 % (1607617)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.28 % (1607640)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1145411828:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.28 % (1607640)Instruction limit reached!
% 0.09/0.28 % (1607640)------------------------------
% 0.09/0.28 % (1607640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1607640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1607640)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1607640)Termination reason: Instruction limit
% 0.09/0.28 % (1607640)Termination phase: Saturation
% 0.09/0.28 % (1607640)Time elapsed: 0.001 s
% 0.09/0.28 % (1607640)Peak memory usage: 11 MB
% 0.09/0.28 % (1607640)Instructions burned: 3 (million)
% 0.09/0.28 % (1607644)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.28 % (1607644)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
% 0.09/0.28 % (1607639)lrs+10_16_si=on:nwc=1.5:random_seed=2344997800:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.28 % (1607638)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3368200242:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.28 % (1607642)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3419898843:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.28 % (1607643)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=303074888:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.28 % (1607641)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=2558057325: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)
% 0.09/0.28 % (1607644)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=2860676054:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.28 % (1607642)Refutation not found, incomplete strategy
% 0.09/0.28 % (1607642)------------------------------
% 0.09/0.28 % (1607642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1607642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1607642)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1607642)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.28 % (1607642)Time elapsed: 0.002 s
% 0.09/0.28 % (1607642)Peak memory usage: 12 MB
% 0.09/0.28 % (1607642)Instructions burned: 3 (million)
% 0.09/0.28 % (1607641)Refutation not found, incomplete strategy
% 0.09/0.28 % (1607641)------------------------------
% 0.09/0.28 % (1607641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1607638) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607617-1607638"...
% 0.09/0.28 % (1607641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1607641)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1607641)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.28 % (1607641)Time elapsed: 0.003 s
% 0.09/0.28 % (1607641)Peak memory usage: 12 MB
% 0.09/0.28 % (1607642)------------------------------
% 0.09/0.28 % (1607642)------------------------------
% 0.09/0.28 % (1607641)Instructions burned: 4 (million)
% 0.09/0.28 % (1607641)------------------------------
% 0.09/0.28 % (1607641)------------------------------
% 0.09/0.28 % (1607638)...printing done.
% 0.09/0.28 % (1607643) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607617-1607643"...
% 0.09/0.28 % (1607646)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=500287635:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.09/0.28 % (1607644)Refutation not found, incomplete strategy
% 0.09/0.28 % (1607644)------------------------------
% 0.09/0.28 % (1607644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1607644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1607644)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1607644)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.28 % (1607644)Time elapsed: 0.007 s
% 0.09/0.28 % (1607644)Peak memory usage: 12 MB
% 0.09/0.28 % (1607644)Instructions burned: 9 (million)
% 0.09/0.28 % (1607646)Instruction limit reached!
% 0.09/0.28 % (1607646)------------------------------
% 0.09/0.28 % (1607646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1607646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1607646)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1607646)Termination reason: Instruction limit
% 0.09/0.28 % (1607646)Termination phase: Saturation
% 0.09/0.28 % (1607646)Time elapsed: 0.001 s
% 0.09/0.28 % (1607646)Peak memory usage: 12 MB
% 0.09/0.28 % (1607646)Instructions burned: 2 (million)
% 0.09/0.28 % (1607644)------------------------------
% 0.09/0.28 % (1607644)------------------------------
% 0.09/0.28 % (1607639) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607617-1607639"...
% 0.09/0.28 % (1607643)...printing done.
% 0.09/0.28 % (1607638)Refutation found. Thanks to Tanya!
% 0.09/0.28 % SZS status Theorem for theBenchmark
% 0.09/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.28 % (1607638)------------------------------
% 0.09/0.28 % (1607638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1607638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1607638)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1607638)Termination reason: Refutation
% 0.09/0.28 % (1607638)Time elapsed: 0.006 s
% 0.09/0.28 % (1607638)Peak memory usage: 13 MB
% 0.09/0.28 % (1607638)Instructions burned: 8 (million)
% 0.09/0.28 % (1607617)Success in time 0.044 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------