%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV497^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:38:45 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 297 ( 87 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 949 ( 46 ~; 33 |; 19 &; 834 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 95 ( 95 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 3 con; 0-6 aty)
% Number of variables : 136 ( 0 ^; 120 !; 16 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(type_def_8,type,
sK2: $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/iterate/support':
!>[X0: $tType,X1: $tType] : ( ( X0 > X0 > X0 ) > ( X1 > X0 ) > ( X1 > $o ) > X1 > $o ) ).
thf(func_def_5,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_6,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_7,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_8,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_12,type,
sK3: sK1 > sK1 > sK1 ).
thf(func_def_13,type,
sK4: sK2 > $o ).
thf(func_def_14,type,
sK5: sK2 > sK1 ).
thf(func_def_15,type,
sK6: sK2 ).
thf(func_def_16,type,
sK7: sK0 > sK1 ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ( ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) )
& ! [X3: X0 > X1,X5: X0 > $o,X4: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
& ( 'const/iterate/monoidal' @ X1 @ X2 ) )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X4 @ X5 ) @ X3 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( X2 @ ( X3 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_GEN_') ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X4: X1 > $o,X3: X1 > X0] :
( ( 'const/sets/FINITE' @ X1 @ X4 )
=> ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_SUPPORT_') ).
thf(f3,conjecture,
! [X1: $tType,X2: $tType,X0: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X6: X1 > $o,X4: X1 > X2,X5: X1] :
( ( 'const/sets/FINITE' @ X1 @ X6 )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) ) )
& ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(f4,negated_conjecture,
~ ! [X1: $tType,X2: $tType,X0: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X6: X1 > $o,X4: X1 > X2,X5: X1] :
( ( 'const/sets/FINITE' @ X1 @ X6 )
=> ( ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X5 @ X6 ) @ X4 )
= ( 'const/class/COND' @ X2 @ ( 'const/sets/IN' @ X1 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) @ ( X3 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X2 @ X3 @ X6 @ X4 ) ) ) ) )
& ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ( ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) )
& ! [X4: X0 > X1,X5: X0 > $o,X6: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X5 ) )
& ( 'const/iterate/monoidal' @ X1 @ X2 ) )
=> ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X6 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) @ ( X2 @ ( X4 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X6 @ X5 ) @ X4 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ( ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) )
& ! [X4: X0 > X1,X5: X0 > $o,X6: X0] :
( ( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X5 ) )
= $true ) )
=> ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X6 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) @ ( X2 @ ( X4 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X6 @ X5 ) @ X4 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > $o,X4: X1 > X0] :
( ( 'const/sets/FINITE' @ X1 @ X3 )
=> ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X3: X1 > $o,X2: X0 > X0 > X0,X4: X1 > X0] :
( ( ( 'const/sets/FINITE' @ X1 @ X3 )
= $true )
=> ( $true
= ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X3 )
=> ( ! [X4: X0 > $o,X5: X0 > X1,X6: X0] :
( ( 'const/sets/FINITE' @ X0 @ X4 )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X6 @ X4 ) @ X5 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X6 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ X4 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ X4 @ X5 ) ) ) ) )
& ! [X7: X2 > X1] :
( ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ 'const/sets/EMPTY' @ X2 @ X7 )
= ( 'const/iterate/neutral' @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X1: $tType,X2: $tType,X0: $tType,X3: X1 > X1 > X1] :
( ( $true
= ( 'const/iterate/monoidal' @ X1 @ X3 ) )
=> ( ! [X4: X0 > $o,X6: X0,X5: X0 > X1] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X6 @ X4 ) @ X5 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X6 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ X4 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ X4 @ X5 ) ) ) ) )
& ! [X7: X2 > X1] :
( ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ 'const/sets/EMPTY' @ X2 @ X7 )
= ( 'const/iterate/neutral' @ X1 @ X3 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X3: X1 > $o,X4: X1 > X0,X2: X0 > X0 > X0] :
( ( $true
= ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) )
| ( ( 'const/sets/FINITE' @ X1 @ X3 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) )
& ! [X4: X0 > X1,X5: X0 > $o,X6: X0] :
( ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X6 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) @ ( X2 @ ( X4 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X6 @ X5 ) @ X4 ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X5 ) )
!= $true ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ! [X6: X0,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X5 ) )
!= $true )
| ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X6 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) @ ( X2 @ ( X4 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X6 @ X5 ) @ X4 ) ) )
& ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
? [X2: $tType,X1: $tType,X0: $tType,X3: X1 > X1 > X1] :
( ( ? [X4: X0 > $o,X5: X0 > X1,X6: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ( ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X6 @ X4 ) @ X5 )
!= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X6 @ X4 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ X4 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ X4 @ X5 ) ) ) ) )
| ? [X7: X2 > X1] :
( ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ 'const/sets/EMPTY' @ X2 @ X7 )
!= ( 'const/iterate/neutral' @ X1 @ X3 ) ) )
& ( $true
= ( 'const/iterate/monoidal' @ X1 @ X3 ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ! [X3: X0,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X5 ) )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X3 @ X5 ) @ X4 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) @ ( X2 @ ( X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) ) ) ) )
& ! [X6: X0 > X1] :
( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(rectify,[],[f13]) ).
thf(f16,plain,
? [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X1 > X1] :
( ( ? [X4: X2 > $o,X5: X2 > X1,X6: X2] :
( ( $true
= ( 'const/sets/FINITE' @ X2 @ X4 ) )
& ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X2 @ X6 @ X4 ) @ ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ X4 @ X5 ) @ ( X3 @ ( X5 @ X6 ) @ ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ X4 @ X5 ) ) )
!= ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ ( 'const/sets/INSERT' @ X2 @ X6 @ X4 ) @ X5 ) ) )
| ? [X7: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 )
!= ( 'const/iterate/neutral' @ X1 @ X3 ) ) )
& ( $true
= ( 'const/iterate/monoidal' @ X1 @ X3 ) ) ),
inference(rectify,[],[f14]) ).
thf(f17,plain,
( ( ( ( ( 'const/sets/FINITE' @ sK2 @ sK4 )
= $true )
& ( ( 'const/class/COND' @ sK1 @ ( 'const/sets/IN' @ sK2 @ sK6 @ sK4 ) @ ( 'const/iterate/iterate' @ sK2 @ sK1 @ sK3 @ sK4 @ sK5 ) @ ( sK3 @ ( sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK2 @ sK1 @ sK3 @ sK4 @ sK5 ) ) )
!= ( 'const/iterate/iterate' @ sK2 @ sK1 @ sK3 @ ( 'const/sets/INSERT' @ sK2 @ sK6 @ sK4 ) @ sK5 ) ) )
| ( ( 'const/iterate/iterate' @ sK0 @ sK1 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK1 @ sK3 ) ) )
& ( ( 'const/iterate/monoidal' @ sK1 @ sK3 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f16]) ).
thf(f18,plain,
! [X0: $tType,X1: $tType,X2: X1 > $o,X3: X1 > X0,X4: X0 > X0 > X0] :
( ( $true
= ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X4 @ X3 @ X2 ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X2 ) ) ),
inference(rectify,[],[f11]) ).
thf(f19,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X6: X0 > X1] :
( ( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X3 @ X5 ) @ X4 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) @ ( X2 @ ( X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X5 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f21,plain,
( ( 'const/iterate/monoidal' @ sK1 @ sK3 )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f22,plain,
( ( ( 'const/class/COND' @ sK1 @ ( 'const/sets/IN' @ sK2 @ sK6 @ sK4 ) @ ( 'const/iterate/iterate' @ sK2 @ sK1 @ sK3 @ sK4 @ sK5 ) @ ( sK3 @ ( sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK2 @ sK1 @ sK3 @ sK4 @ sK5 ) ) )
!= ( 'const/iterate/iterate' @ sK2 @ sK1 @ sK3 @ ( 'const/sets/INSERT' @ sK2 @ sK6 @ sK4 ) @ sK5 ) )
| ( ( 'const/iterate/iterate' @ sK0 @ sK1 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK1 @ sK3 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f23,plain,
( ( ( 'const/iterate/iterate' @ sK0 @ sK1 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK1 @ sK3 ) )
| ( ( 'const/sets/FINITE' @ sK2 @ sK4 )
= $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f24,plain,
! [X1: $tType,X0: $tType,X2: X1 > $o,X3: X1 > X0,X4: X0 > X0 > X0] :
( ( $true
= ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X4 @ X3 @ X2 ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f26,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X3 @ X5 ) @ X4 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) @ ( X2 @ ( X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X4 @ X5 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(duplicate_literal_removal,[],[f20]) ).
thf(f28,plain,
( ( ( 'const/sets/FINITE' @ sK2 @ sK4 )
= $true )
| ( ( 'const/iterate/neutral' @ sK1 @ sK3 )
!= ( 'const/iterate/neutral' @ sK1 @ sK3 ) )
| ( ( 'const/iterate/monoidal' @ sK1 @ sK3 )
!= $true ) ),
inference(superposition,[],[f23,f19]) ).
thf(f29,plain,
( ( ( 'const/iterate/monoidal' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/sets/FINITE' @ sK2 @ sK4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f30,plain,
( ( 'const/sets/FINITE' @ sK2 @ sK4 )
= $true ),
inference(forward_subsumption_resolution,[],[f29,f21]) ).
thf(f46,plain,
( ( ( 'const/iterate/monoidal' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/iterate/iterate' @ sK0 @ sK1 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK1 @ sK3 ) )
| ( ( 'const/sets/FINITE' @ sK2 @ ( 'const/iterate/support' @ sK1 @ sK2 @ sK3 @ sK5 @ sK4 ) )
!= $true )
| ( ( 'const/iterate/iterate' @ sK2 @ sK1 @ sK3 @ ( 'const/sets/INSERT' @ sK2 @ sK6 @ sK4 ) @ sK5 )
!= ( 'const/iterate/iterate' @ sK2 @ sK1 @ sK3 @ ( 'const/sets/INSERT' @ sK2 @ sK6 @ sK4 ) @ sK5 ) ) ),
inference(superposition,[],[f22,f26]) ).
thf(f51,plain,
( ( ( 'const/sets/FINITE' @ sK2 @ ( 'const/iterate/support' @ sK1 @ sK2 @ sK3 @ sK5 @ sK4 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ sK1 @ sK3 )
!= $true )
| ( ( 'const/iterate/iterate' @ sK0 @ sK1 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 )
!= ( 'const/iterate/neutral' @ sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f55,plain,
( ( ( 'const/sets/FINITE' @ sK2 @ ( 'const/iterate/support' @ sK1 @ sK2 @ sK3 @ sK5 @ sK4 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ sK1 @ sK3 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f51,f19]) ).
thf(f56,plain,
( ( 'const/sets/FINITE' @ sK2 @ ( 'const/iterate/support' @ sK1 @ sK2 @ sK3 @ sK5 @ sK4 ) )
!= $true ),
inference(forward_subsumption_resolution,[],[f55,f21]) ).
thf(f57,plain,
( ( $true != $true )
| ( ( 'const/sets/FINITE' @ sK2 @ sK4 )
!= $true ) ),
inference(superposition,[],[f56,f24]) ).
thf(f58,plain,
( ( 'const/sets/FINITE' @ sK2 @ sK4 )
!= $true ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f59,plain,
$false,
inference(forward_subsumption_resolution,[],[f58,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV497^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n013.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 15:53:06 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 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
% 0.20/0.29 % (2284206)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (2284214)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=4236021066: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)
% 0.20/0.29 % (2284217)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (2284217)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
% 0.20/0.29 % (2284213)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1081584674:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (2284211)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3502217643:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (2284212)lrs+10_16_si=on:nwc=1.5:random_seed=2493465681:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (2284215)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1985851378:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (2284216)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=340319043:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (2284217)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=1643319778:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (2284213)Instruction limit reached!
% 0.20/0.29 % (2284213)------------------------------
% 0.20/0.29 % (2284213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2284213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2284213)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2284213)Termination reason: Instruction limit
% 0.20/0.29 % (2284213)Termination phase: Saturation
% 0.20/0.29 % (2284213)Time elapsed: 0.002 s
% 0.20/0.29 % (2284213)Peak memory usage: 11 MB
% 0.20/0.29 % (2284213)Instructions burned: 3 (million)
% 0.20/0.29 % (2284215) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2284206-2284215"...
% 0.20/0.29 % (2284212)Instruction limit reached!
% 0.20/0.29 % (2284212)------------------------------
% 0.20/0.29 % (2284212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2284212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2284212)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2284212)Termination reason: Instruction limit
% 0.20/0.29 % (2284212)Termination phase: Saturation
% 0.20/0.29 % (2284212)Time elapsed: 0.011 s
% 0.20/0.29 % (2284212)Peak memory usage: 12 MB
% 0.20/0.29 % (2284212)Instructions burned: 19 (million)
% 0.20/0.29 % (2284215)...printing done.
% 0.20/0.29 % (2284215)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (2284215)------------------------------
% 0.20/0.29 % (2284215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2284215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2284215)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2284215)Termination reason: Refutation
% 0.20/0.29 % (2284215)Time elapsed: 0.011 s
% 0.20/0.29 % (2284215)Peak memory usage: 12 MB
% 0.20/0.29 % (2284215)Instructions burned: 19 (million)
% 0.20/0.29 % (2284206)Success in time 0.053 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------