%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN051^1 : 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 : n014.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 08:20:03 AM UTC 2026
% Result : Theorem 0.11s 0.23s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 32 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 317 ( 12 ~; 3 |; 2 &; 293 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 59 ( 14 ^; 42 !; 3 ?; 59 :)
% 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/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_1,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_2,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_3,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_4,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_5,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
sK0: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_13,type,
sK1: 'type/nums/num' ).
thf(func_def_14,type,
sK2: 'type/nums/num' ).
thf(f1,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X0 )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/SUB_ADD_') ).
thf(f2,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X0 )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/ADD_CLAUSES_0') ).
thf(f3,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ X4 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_OFFSET_') ).
thf(f4,conjecture,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_OFFSET_0_') ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X0 )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X0 )
= $true )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ X4 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ X0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X2 )
= $true )
=> ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 )
| ( ( 'const/arith/<=' @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f13,plain,
? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ X1 ) ) ) )
& ( ( 'const/arith/<=' @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) ) )
& ( $true
= ( 'const/arith/<=' @ sK1 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
thf(f15,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X0 )
!= $true )
| ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
! [X0: 'type/nums/num'] :
( ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X0 )
= X0 ),
inference(cnf_transformation,[],[f2]) ).
thf(f17,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
( $true
= ( 'const/arith/<=' @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( ( $true != $true )
| ( sK2
= ( 'const/arith/+' @ ( 'const/arith/-' @ sK2 @ sK1 ) @ sK1 ) ) ),
inference(constrained_superposition,[],[f15,f18]) ).
thf(f32,plain,
( sK2
= ( 'const/arith/+' @ ( 'const/arith/-' @ sK2 @ sK1 ) @ sK1 ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f34,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] :
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X0 @ sK1 ) @ sK2 ) @ X1 ) ),
inference(constrained_superposition,[],[f17,f32]) ).
thf(f46,plain,
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ sK1 ) @ sK2 )
@ ^ [Y0: 'type/nums/num'] :
( sK0
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 ) ) ) ),
inference(constrained_superposition,[],[f19,f34]) ).
thf(f52,plain,
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ sK1 ) @ sK2 ) @ sK0 ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f55,plain,
( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ),
inference(forward_demodulation,[],[f52,f16]) ).
thf(f56,plain,
$false,
inference(trivial_inequality_removal,[],[f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN051^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.16 % Computer : n014.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 13:07:16 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.20 Running first-order model finding
% 0.11/0.20 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
% 0.11/0.23 % (2623679)Will run a generic schedule for satisfiability detection.
% 0.11/0.23 % (2623695)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2414559678:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.23 % (2623690)% WARNING: option uhcvi not known.
% 0.11/0.23 % (2623695) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2623679-2623695"...
% 0.11/0.23 % (2623695)...printing done.
% 0.11/0.23 % (2623695)Refutation found. Thanks to Tanya!
% 0.11/0.23 % SZS status Theorem for theBenchmark
% 0.11/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.23 % (2623695)------------------------------
% 0.11/0.23 % (2623695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.23 % (2623695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.23 % (2623695)CaDiCaL version: 2.1.3
% 0.11/0.23 % (2623695)Termination reason: Refutation
% 0.11/0.23 % (2623695)Time elapsed: 0.004 s
% 0.11/0.23 % (2623695)Peak memory usage: 12 MB
% 0.11/0.23 % (2623695)Instructions burned: 11 (million)
% 0.11/0.23 % (2623679)Success in time 0.021 s
% 0.11/0.23 % Vampire exiting
%------------------------------------------------------------------------------