%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA068^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 07:45:50 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 187 ( 47 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 245 ( 30 ~; 16 |; 4 &; 187 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 3 con; 0-4 aty)
% ( 0 !!; 3 ??; 0 @@+; 0 @@-)
% Number of variables : 62 ( 8 ^; 52 !; 2 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_1,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/SETSPEC':
!>[X0: $tType] : ( X0 > $o > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/INFINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/GSPEC':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).
thf(func_def_5,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_10,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
! [X0: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ X1 @ ( 'const/realax/real_le' @ X0 @ X2 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_REAL_INTERVAL_1') ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_UNIV_') ).
thf(f3,axiom,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o] :
( ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) )
= ( 'const/sets/INFINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INFINITE_') ).
thf(f5,conjecture,
'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/real_INFINITE_') ).
thf(f6,negated_conjecture,
~ ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ X1 @ ( 'const/realax/real_le' @ X0 @ X2 ) @ X2 ) ) ),
inference(rectify,[],[f1]) ).
thf(f12,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 ) )
=> ( 'const/sets/FINITE' @ X0 @ X2 ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) )
= ( 'const/sets/INFINITE' @ X0 @ X1 ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
<=> ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(flattening,[],[f8]) ).
thf(f18,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(flattening,[],[f12]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
<=> ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true ) ),
inference(flattening,[],[f16]) ).
thf(f20,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f21,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/INFINITE' @ X0 @ X1 )
!= $true ) )
& ( ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ) ),
inference(nnf_transformation,[],[f19]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(rectify,[],[f21]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f26,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f27,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f28,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f29,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f32,plain,
( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f29,f24]) ).
thf(f33,plain,
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f36,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ 'const/sets/UNIV' @ X0 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f27,f28]) ).
thf(f37,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ 'const/sets/UNIV' @ X0 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f38,plain,
! [X0: 'type/realax/real' > $o] :
( ( $true != $true )
| ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) ) ),
inference(constrained_superposition,[],[f37,f33]) ).
thf(f39,plain,
! [X0: 'type/realax/real' > $o] :
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f46,plain,
$true != $true,
inference(constrained_superposition,[],[f26,f39]) ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA068^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:38:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 % (2425858)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2425863)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2615794414:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (2425863) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2425858-2425863"...
% 0.20/0.27 % (2425863)...printing done.
% 0.20/0.27 % (2425863)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2425863)------------------------------
% 0.20/0.27 % (2425863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2425863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2425863)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2425863)Termination reason: Refutation
% 0.20/0.27 % (2425863)Time elapsed: 0.002 s
% 0.20/0.27 % (2425863)Peak memory usage: 12 MB
% 0.20/0.27 % (2425863)Instructions burned: 3 (million)
% 0.20/0.27 % (2425858)Success in time 0.033 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------