%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV502^1 : 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 : n004.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 08:39:36 AM UTC 2026
% Result : Theorem 0.27s 0.36s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 54 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 470 ( 25 ~; 16 |; 13 &; 406 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 3 con; 0-5 aty)
% Number of variables : 73 ( 0 ^; 65 !; 8 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/DELETE':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > X0 > $o ) ).
thf(func_def_3,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_4,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_5,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_6,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_10,type,
sK1: sK0 > 'type/nums/num' ).
thf(func_def_11,type,
sK2: sK0 > $o ).
thf(func_def_12,type,
sK3: sK0 ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/nsum_') ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X4 ) )
=> ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_DELETE_') ).
thf(f3,axiom,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_ADD_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_DELETE_') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
& ( 'const/sets/FINITE' @ X0 @ X4 ) )
=> ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true ) )
=> ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
inference(rectify,[],[f3]) ).
thf(f9,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
=> ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
? [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
!= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f15,plain,
? [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o,X3: X0] :
( ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
!= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( ( 'const/arith/+' @ ( sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ sK1 ) )
!= ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK1 ) )
& ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
& ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
thf(f17,plain,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f18,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f20,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( ( 'const/arith/+' @ ( sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ sK1 ) )
!= ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( ( 'const/arith/+' @ ( sK1 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ sK1 ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK1 ) ),
inference(definition_unfolding,[],[f22,f17,f17]) ).
thf(f33,plain,
! [X0: $tType,X2: sK0 > X0,X1: X0 > X0 > X0] :
( ( $true != $true )
| ( ( X1 @ ( X2 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ X2 ) )
= ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK2 @ X2 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f18,f21]) ).
thf(f36,plain,
! [X0: $tType,X2: sK0 > X0,X1: X0 > X0 > X0] :
( ( ( X1 @ ( X2 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ X2 ) )
= ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK2 @ X2 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f37,plain,
! [X0: $tType,X2: sK0 > X0,X1: X0 > X0 > X0] :
( ( $true
!= ( 'const/iterate/monoidal' @ X0 @ X1 ) )
| ( ( X1 @ ( X2 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ X2 ) )
= ( 'const/iterate/iterate' @ sK0 @ X0 @ X1 @ sK2 @ X2 ) ) ),
inference(forward_subsumption_resolution,[],[f36,f20]) ).
thf(f38,plain,
! [X0: sK0 > 'type/nums/num'] :
( ( $true != $true )
| ( ( 'const/arith/+' @ ( X0 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ X0 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ X0 ) ) ),
inference(constrained_superposition,[],[f37,f19]) ).
thf(f41,plain,
! [X0: sK0 > 'type/nums/num'] :
( ( 'const/arith/+' @ ( X0 @ sK3 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK3 ) @ X0 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ X0 ) ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f43,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK1 )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK1 ) ),
inference(constrained_superposition,[],[f25,f41]) ).
thf(f44,plain,
$false,
inference(trivial_inequality_removal,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV502^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n004.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 15:54:07 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.27/0.32 Running first-order model finding
% 0.27/0.32 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
% 0.27/0.36 % (1467667)Will run a generic schedule for satisfiability detection.
% 0.27/0.36 % (1467677)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3182564214:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.27/0.36 % (1467676)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3664149079:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.27/0.36 % (1467676)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.27/0.36 % (1467677) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1467667-1467677"...
% 0.27/0.36 % (1467677)...printing done.
% 0.27/0.36 % (1467673)% WARNING: option uhcvi not known.
% 0.27/0.36 % (1467677)Refutation found. Thanks to Tanya!
% 0.27/0.36 % SZS status Theorem for theBenchmark
% 0.27/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/0.36 % (1467677)------------------------------
% 0.27/0.36 % (1467677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.36 % (1467677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.36 % (1467677)CaDiCaL version: 2.1.3
% 0.27/0.36 % (1467677)Termination reason: Refutation
% 0.27/0.36 % (1467677)Time elapsed: 0.005 s
% 0.27/0.36 % (1467677)Peak memory usage: 12 MB
% 0.27/0.36 % (1467677)Instructions burned: 6 (million)
% 0.27/0.36 % (1467667)Success in time 0.029 s
% 0.27/0.36 % Vampire exiting
%------------------------------------------------------------------------------