%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA119^1 : 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 : n002.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 07:45:57 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 38 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 655 ( 14 ~; 5 |; 3 &; 626 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 57 ( 14 ^; 39 !; 4 ?; 57 :)
% 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(func_def_0,type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_1,type,
'const/realax/real_pow': 'type/realax/real' > 'type/nums/num' > 'type/realax/real' ).
thf(func_def_2,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_3,type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf(func_def_4,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_5,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/nums/BIT1': '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/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_10,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_11,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
sK0: 'type/nums/num' ).
thf(func_def_18,type,
sK1: 'type/realax/real' ).
thf(f1,axiom,
! [X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ X0 ) @ X1 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/calc_int/REAL_MUL_LNEG_') ).
thf(f2,axiom,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_R1_') ).
thf(f3,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ X0 @ X1 ) )
= ( 'const/realax/real_sub' @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_NEG_SUB_') ).
thf(f4,conjecture,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/REAL_SUB_POW_L1_') ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ! [X1: 'type/nums/num',X0: 'type/realax/real'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
= $true )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [X2: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
! [X1: 'type/nums/num',X0: 'type/realax/real'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
= $true )
=> ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X1: 'type/nums/num',X0: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ X1 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) )
| ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
? [X1: 'type/nums/num',X0: 'type/realax/real'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X1 )
= $true )
& ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ X1 ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X1 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f12,plain,
? [X0: 'type/nums/num',X1: 'type/realax/real'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X0 )
= $true )
& ( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X1 @ X0 ) )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X1 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X1 @ Y0 ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f13,plain,
( ( $true
= ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sK0 ) )
& ( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sK1 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ sK1 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK1 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X1 @ X0 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ X1 ) @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f15,plain,
! [X0: 'type/nums/num',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X1 @ X0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X1 @ Y0 ) ) ) )
| ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X0 )
!= $true ) ),
inference(rectify,[],[f10]) ).
thf(f16,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sK1 )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ sK1 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
( $true
= ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ sK0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ X1 @ X0 ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_neg' @ X1 ) @ X0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ X0 @ X1 ) )
= ( 'const/realax/real_sub' @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f20,plain,
! [X0: 'type/nums/num',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X1 @ X0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_pow' @ X1 @ Y0 ) ) ) )
| ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
! [X0: 'type/nums/num',X1: 'type/realax/real'] :
( ( ( 'const/arith/<=' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) @ X0 )
!= $true )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X1 @ X0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X1 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f24,plain,
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ sK1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ sK1 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f25,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ X1 ) @ X2 )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X1 @ X0 ) @ X2 ) ) ),
inference(constrained_superposition,[],[f18,f19]) ).
thf(f31,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) ) ) ),
inference(constrained_superposition,[],[f23,f17]) ).
thf(f32,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ X0 @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f37,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) )
= ( 'const/realax/real_neg' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_pow' @ X0 @ sK0 ) @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) ) ),
inference(constrained_superposition,[],[f25,f32]) ).
thf(f41,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK0 @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) @ ( 'const/realax/real_pow' @ X0 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ X0 @ sK0 ) ) ),
inference(forward_demodulation,[],[f37,f19]) ).
thf(f49,plain,
( ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK1 @ sK0 ) )
!= ( 'const/realax/real_sub' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) @ ( 'const/realax/real_pow' @ sK1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f24,f41]) ).
thf(f51,plain,
$false,
inference(trivial_inequality_removal,[],[f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA119^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 17:45:07 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.21 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
% 0.07/0.26 % (1628698)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.26 % (1628704)lrs+10_16_si=on:nwc=1.5:random_seed=2894880065:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.07/0.26 % (1628704) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1628698-1628704"...
% 0.07/0.26 % (1628704)...printing done.
% 0.07/0.26 % (1628704)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.26 % (1628704)------------------------------
% 0.28/0.26 % (1628704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.26 % (1628704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.26 % (1628704)CaDiCaL version: 2.1.3
% 0.28/0.26 % (1628704)Termination reason: Refutation
% 0.28/0.26 % (1628704)Time elapsed: 0.005 s
% 0.28/0.26 % (1628704)Peak memory usage: 12 MB
% 0.28/0.26 % (1628704)Instructions burned: 16 (million)
% 0.28/0.26 % (1628698)Success in time 0.038 s
% 0.28/0.26 % Vampire exiting
%------------------------------------------------------------------------------