%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV494^1 : 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 : n006.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 08:38:44 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 231 ( 10 ~; 3 |; 3 &; 208 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 20 !; 4 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_2,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_3,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_4,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_5,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_6,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_11,type,
sK0: 'type/nums/num' ).
thf(func_def_12,type,
sK1: 'type/nums/num' ).
thf(func_def_13,type,
sK2: 'type/nums/num' ).
thf(f1,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ X0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/SUC_SUB1_') ).
thf(f2,axiom,
! [X1: 'type/nums/num',X0: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ X1 )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NUMSEG_RREC_') ).
thf(f3,conjecture,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NUMSEG_REC_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= $true )
=> ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X0 )
=> ( ( 'const/iterate/..' @ X1 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ ( 'const/iterate/..' @ X1 @ ( 'const/arith/-' @ X0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X1: 'type/nums/num',X0: 'type/nums/num'] :
( ( $true
= ( 'const/arith/<=' @ X1 @ X0 ) )
=> ( ( 'const/iterate/..' @ X1 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ ( 'const/iterate/..' @ X1 @ ( 'const/arith/-' @ X0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true
!= ( 'const/arith/<=' @ X1 @ X0 ) )
| ( ( 'const/iterate/..' @ X1 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ ( 'const/iterate/..' @ X1 @ ( 'const/arith/-' @ X0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f10,plain,
? [X1: 'type/nums/num',X0: 'type/nums/num'] :
( ( ( 'const/iterate/..' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X1 ) @ ( 'const/iterate/..' @ X0 @ X1 ) ) )
& ( ( 'const/arith/<=' @ X0 @ ( 'const/nums/SUC' @ X1 ) )
= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f11,plain,
? [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ X0 ) @ ( 'const/iterate/..' @ X1 @ X0 ) )
!= ( 'const/iterate/..' @ X1 @ ( 'const/nums/SUC' @ X0 ) ) )
& ( $true
= ( 'const/arith/<=' @ X1 @ ( 'const/nums/SUC' @ X0 ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
( ( ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK0 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK0 ) @ ( 'const/iterate/..' @ sK1 @ sK0 ) ) )
& ( $true
= ( 'const/arith/<=' @ sK1 @ ( 'const/nums/SUC' @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
thf(f13,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true
!= ( 'const/arith/<=' @ X1 @ X0 ) )
| ( ( 'const/iterate/..' @ X1 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ ( 'const/iterate/..' @ X1 @ ( 'const/arith/-' @ X0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( $true
= ( 'const/arith/<=' @ sK1 @ ( 'const/nums/SUC' @ sK0 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f15,plain,
( ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK0 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK0 ) @ ( 'const/iterate/..' @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
! [X0: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ X0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= X0 ),
inference(cnf_transformation,[],[f1]) ).
thf(f44,plain,
( ( $true != $true )
| ( ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK0 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK0 ) @ ( 'const/iterate/..' @ sK1 @ ( 'const/arith/-' @ ( 'const/nums/SUC' @ sK0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f13,f14]) ).
thf(f45,plain,
( ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK0 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK0 ) @ ( 'const/iterate/..' @ sK1 @ ( 'const/arith/-' @ ( 'const/nums/SUC' @ sK0 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f46,plain,
( ( 'const/iterate/..' @ sK1 @ ( 'const/nums/SUC' @ sK0 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sK0 ) @ ( 'const/iterate/..' @ sK1 @ sK0 ) ) ),
inference(forward_demodulation,[],[f45,f16]) ).
thf(f47,plain,
$false,
inference(forward_subsumption_resolution,[],[f46,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV494^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:52:55 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
% 0.08/0.23 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
% 0.20/0.28 % (899762)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (899767)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3272536737:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (899767) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-899762-899767"...
% 0.20/0.28 % (899767)...printing done.
% 0.20/0.28 % (899767)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (899767)------------------------------
% 0.20/0.28 % (899767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (899767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (899767)CaDiCaL version: 2.1.3
% 0.20/0.28 % (899767)Termination reason: Refutation
% 0.20/0.28 % (899767)Time elapsed: 0.002 s
% 0.20/0.28 % (899767)Peak memory usage: 12 MB
% 0.20/0.28 % (899767)Instructions burned: 3 (million)
% 0.20/0.28 % (899762)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------