%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV507^1 : 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 : n015.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 08:38:46 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 321 ( 12 ~; 6 |; 5 &; 292 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 3 con; 0-5 aty)
% Number of variables : 56 ( 0 ^; 54 !; 2 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
sK0: $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/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_5,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_6,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_8,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_9,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_10,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_11,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_12,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_16,type,
sK1: sK0 > 'type/realax/real' ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X3: X2 > X2 > X2] :
( ( 'const/iterate/monoidal' @ X2 @ X3 )
=> ( ! [X4: X0 > X2] :
( ( 'const/iterate/iterate' @ X0 @ X2 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X2 @ X3 ) )
& ! [X5: X1,X6: X1 > $o,X4: X1 > X2] :
( ( '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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(f2,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f3,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(f4,axiom,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NEUTRAL_REAL_ADD_') ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_CLAUSES_0') ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X3 )
=> ( ! [X4: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X1 @ X3 ) )
& ! [X5: X2,X6: X2 > $o,X7: X2 > X1] :
( ( 'const/sets/FINITE' @ X2 @ X6 )
=> ( ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ ( 'const/sets/INSERT' @ X2 @ X5 @ X6 ) @ X7 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X2 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ X6 @ X7 ) @ ( X3 @ ( X7 @ X5 ) @ ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ X6 @ X7 ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X1 > X1] :
( ( $true
= ( 'const/iterate/monoidal' @ X1 @ X3 ) )
=> ( ! [X7: X2 > X1,X5: X2,X6: X2 > $o] :
( ( $true
= ( 'const/sets/FINITE' @ X2 @ X6 ) )
=> ( ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ ( 'const/sets/INSERT' @ X2 @ X5 @ X6 ) @ X7 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X2 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ X6 @ X7 ) @ ( X3 @ ( X7 @ X5 ) @ ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ X6 @ X7 ) ) ) ) )
& ! [X4: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X1 @ X3 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X1: $tType,X2: $tType,X0: $tType,X3: X1 > X1 > X1] :
( ( $true
!= ( 'const/iterate/monoidal' @ X1 @ X3 ) )
| ( ! [X4: X0 > X1] :
( ( 'const/iterate/iterate' @ X0 @ X1 @ X3 @ 'const/sets/EMPTY' @ X0 @ X4 )
= ( 'const/iterate/neutral' @ X1 @ X3 ) )
& ! [X6: X2 > $o,X7: X2 > X1,X5: X2] :
( ( ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ ( 'const/sets/INSERT' @ X2 @ X5 @ X6 ) @ X7 )
= ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X2 @ X5 @ X6 ) @ ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ X6 @ X7 ) @ ( X3 @ ( X7 @ X5 ) @ ( 'const/iterate/iterate' @ X2 @ X1 @ X3 @ X6 @ X7 ) ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ X2 @ X6 ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
? [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ X0 @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X0 > X0] :
( ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
| ( ! [X4: X2 > X0] :
( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ 'const/sets/EMPTY' @ X2 @ X4 )
= ( 'const/iterate/neutral' @ X0 @ X3 ) )
& ! [X5: X1 > $o,X6: X1 > X0,X7: X1] :
( ( ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ X1 @ X7 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X5 @ X6 ) @ ( X3 @ ( X6 @ X7 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ X5 @ X6 ) ) )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X3 @ ( 'const/sets/INSERT' @ X1 @ X7 @ X5 ) @ X6 ) )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X5 ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f14,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f16,plain,
! [X0: $tType,X2: $tType,X3: X0 > X0 > X0,X4: X2 > X0] :
( ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X3 ) )
| ( ( 'const/iterate/iterate' @ X2 @ X0 @ X3 @ 'const/sets/EMPTY' @ X2 @ X4 )
= ( 'const/iterate/neutral' @ X0 @ X3 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f18,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/sum' @ sK0 @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f20,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
( ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ sK0 @ sK1 ) ),
inference(definition_unfolding,[],[f18,f19]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f16,f20]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ 'const/sets/EMPTY' @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[],[f24]) ).
thf(f26,plain,
( ( 'const/iterate/neutral' @ 'type/realax/real' @ 'const/realax/real_add' )
!= ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(constrained_superposition,[],[f23,f25]) ).
thf(f27,plain,
$false,
inference(forward_subsumption_resolution,[],[f26,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV507^1 : 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 : n015.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 15:57:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 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
% 0.20/0.27 % (3705871)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (3705877)lrs+10_16_si=on:nwc=1.5:random_seed=264362384:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (3705877) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3705871-3705877"...
% 0.20/0.27 % (3705877)...printing done.
% 0.20/0.27 % (3705877)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 % (3705877)------------------------------
% 0.20/0.27 % (3705877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (3705877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (3705877)CaDiCaL version: 2.1.3
% 0.20/0.27 % (3705877)Termination reason: Refutation
% 0.20/0.27 % (3705877)Time elapsed: 0.002 s
% 0.20/0.27 % (3705877)Peak memory usage: 12 MB
% 0.20/0.27 % (3705877)Instructions burned: 4 (million)
% 0.20/0.27 % (3705871)Success in time 0.026 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------