%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV497^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:39:36 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 329 ( 79 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1054 ( 53 ~; 45 |; 16 &; 920 @)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 6 con; 0-6 aty)
% Number of variables : 138 ( 0 sgn 130 !; 8 ?; 138 :)
% 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: sK2 > sK2 > sK2 ).
thf(func_def_13,type,
sK4: sK1 > sK2 ).
thf(func_def_14,type,
sK5: sK1 ).
thf(func_def_15,type,
sK6: sK1 > $o ).
thf(func_def_16,type,
sK7: sK0 > sK2 ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ( ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( '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 ) ) ) ) )
& ! [X3: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= ( 'const/iterate/neutral' @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_GEN_') ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X4 )
=> ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/FINITE_SUPPORT_') ).
thf(f3,conjecture,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( '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/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( '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,X4: X0,X5: X0 > $o] :
( ( ( '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 ) ) ) ) )
& ! [X6: X0 > X1] :
( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ( ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
= $true )
& ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true ) )
=> ( ( '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 ) ) ) ) )
& ! [X6: X0 > X1] :
( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( 'const/sets/FINITE' @ X1 @ X4 )
=> ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X4 )
= $true )
=> ( ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( '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 ) ) ) ) )
& ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ( 'const/iterate/monoidal' @ X2 @ X3 )
= $true )
=> ( ! [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X6 )
= $true )
=> ( ( '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 ) ) ) ) )
& ! [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( '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 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) )
& ! [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(ennf_transformation,[],[f6]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ! [X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( '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 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) )
& ! [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(flattening,[],[f11]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
? [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X2 > X2] :
( ( ? [X4: X1 > X2,X5: X1,X6: X1 > $o] :
( ( ( '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 ) ) ) )
& ( ( 'const/sets/FINITE' @ X1 @ X6 )
= $true ) )
| ? [X7: X0 > X2] :
( ( 'const/iterate/neutral' @ X2 @ X3 )
!= ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X7 ) ) )
& ( ( 'const/iterate/monoidal' @ X2 @ X3 )
= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f15,plain,
( ( ( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK6 ) ) )
| ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 ) ) )
& ( $true
= ( 'const/iterate/monoidal' @ sK2 @ sK3 ) ) ),
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)],[f14]) ).
thf(f16,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X6: X0 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/iterate/neutral' @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X6 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( '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 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o] :
( ( ( 'const/sets/FINITE' @ X1 @ X4 )
!= $true )
| ( ( 'const/sets/FINITE' @ X1 @ ( 'const/iterate/support' @ X0 @ X1 @ X2 @ X3 @ X4 ) )
= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
= ( 'const/iterate/monoidal' @ sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK6 ) )
| ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f21,plain,
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) )
| ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/iterate/support' @ X1 @ X0 @ X2 @ X3 @ X5 ) )
!= $true )
| ( ( '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 ) ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(duplicate_literal_removal,[],[f17]) ).
thf(f26,definition,
( spl8_1
<=> ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f28,plain,
( ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ sK0 @ sK7 ) )
| spl8_1 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f30,definition,
( spl8_2
<=> ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f32,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK6 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f20,f30,f26]) ).
thf(f35,definition,
( spl8_3
<=> ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f37,plain,
( ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ sK5 @ sK6 ) @ sK4 )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) )
| spl8_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( ~ spl8_1
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f21,f35,f26]) ).
thf(f46,plain,
! [X0: $tType,X1: X0 > sK2] :
( ( $true != $true )
| ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
= ( 'const/iterate/iterate' @ X0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f16,f19]) ).
thf(f49,plain,
! [X0: $tType,X1: X0 > sK2] :
( ( 'const/iterate/neutral' @ sK2 @ sK3 )
= ( 'const/iterate/iterate' @ X0 @ sK2 @ sK3 @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f52,plain,
( ( ( 'const/iterate/neutral' @ sK2 @ sK3 )
!= ( 'const/iterate/neutral' @ sK2 @ sK3 ) )
| spl8_1 ),
inference(constrained_superposition,[],[f28,f49]) ).
thf(f53,plain,
( $false
| spl8_1 ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f53]) ).
thf(f55,plain,
( ! [X0: $tType,X2: sK1 > X0,X1: X0 > X0 > X0] :
( ( $true != $true )
| ( $true
= ( 'const/sets/FINITE' @ sK1 @ ( 'const/iterate/support' @ X0 @ sK1 @ X1 @ X2 @ sK6 ) ) ) )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f18,f32]) ).
thf(f56,plain,
( ! [X0: $tType,X2: sK1 > X0,X1: X0 > X0 > X0] :
( $true
= ( 'const/sets/FINITE' @ sK1 @ ( 'const/iterate/support' @ X0 @ sK1 @ X1 @ X2 @ sK6 ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f61,plain,
( ! [X0: $tType,X2: sK1 > X0,X3: sK1,X1: X0 > X0 > X0] :
( ( $true != $true )
| ( ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ ( 'const/sets/INSERT' @ sK1 @ X3 @ sK6 ) @ X2 )
= ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK1 @ X3 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ sK6 @ X2 ) @ ( X1 @ ( X2 @ X3 ) @ ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ sK6 @ X2 ) ) ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X1 ) ) )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f24,f56]) ).
thf(f66,plain,
( ! [X0: $tType,X2: sK1 > X0,X3: sK1,X1: X0 > X0 > X0] :
( ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X1 ) )
| ( ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ ( 'const/sets/INSERT' @ sK1 @ X3 @ sK6 ) @ X2 )
= ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK1 @ X3 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ sK6 @ X2 ) @ ( X1 @ ( X2 @ X3 ) @ ( 'const/iterate/iterate' @ sK1 @ X0 @ X1 @ sK6 @ X2 ) ) ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f87,plain,
( ! [X0: sK1,X1: sK1 > sK2] :
( ( $true != $true )
| ( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ X0 @ sK6 ) @ X1 )
= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ X0 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ X1 ) @ ( sK3 @ ( X1 @ X0 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ X1 ) ) ) ) )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f66,f19]) ).
thf(f91,plain,
( ! [X0: sK1,X1: sK1 > sK2] :
( ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ ( 'const/sets/INSERT' @ sK1 @ X0 @ sK6 ) @ X1 )
= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ X0 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ X1 ) @ ( sK3 @ ( X1 @ X0 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ X1 ) ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f97,plain,
( ( ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) )
!= ( 'const/class/COND' @ sK2 @ ( 'const/sets/IN' @ sK1 @ sK5 @ sK6 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) @ ( sK3 @ ( sK4 @ sK5 ) @ ( 'const/iterate/iterate' @ sK1 @ sK2 @ sK3 @ sK6 @ sK4 ) ) ) )
| ~ spl8_2
| spl8_3 ),
inference(constrained_superposition,[],[f37,f91]) ).
thf(f98,plain,
( $false
| ~ spl8_2
| spl8_3 ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f99,plain,
( ~ spl8_2
| spl8_3 ),
inference(avatar_contradiction_clause,[],[f98]) ).
cnf(s1,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( ~ spl8_1
| ~ spl8_3 ),
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
spl8_1,
inference(sat_conversion,[],[f54]) ).
cnf(s4,plain,
( ~ spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f99]) ).
cnf(s5,plain,
~ spl8_3,
inference(rat,[],[s2,s3]) ).
cnf(s6,plain,
~ spl8_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s3]) ).
thf(f100,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n020.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 15:54:50 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29 % (1215864)Will run a generic schedule for satisfiability detection.
% 0.21/0.29 % (1215871)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2723437863:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.29 % (1215870)% WARNING: option uhcvi not known.
% 0.21/0.29 % (1215869)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2406314571_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.29 % (1215870)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1366195181:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.29 % (1215874)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1746411845:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.29 % (1215872)dis+10_1_sil=32000:sp=arity:random_seed=1385239641:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.29 % (1215873)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3642793734:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.29 % (1215875)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1223506407:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.29 % (1215870)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.29 % (1215873)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.29 % Exception at run slice level
% 0.21/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.29 % (1215870)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.29 % (1215874) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1215864-1215874"...
% 0.21/0.29 % (1215875) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1215864-1215875"...
% 0.21/0.29 % (1215872) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1215864-1215872"...
% 0.21/0.29 % (1215874)...printing done.
% 0.21/0.29 % (1215875)...printing done.
% 0.21/0.29 % (1215874)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (1215874)------------------------------
% 0.21/0.30 % (1215874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1215874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1215874)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1215874)Termination reason: Refutation
% 0.21/0.30 % (1215874)Time elapsed: 0.013 s
% 0.21/0.30 % (1215874)Peak memory usage: 12 MB
% 0.21/0.30 % (1215874)Instructions burned: 20 (million)
% 0.21/0.30 % (1215864)Success in time 0.062 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------