%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM016^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:18:18 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 467 ( 111 equ; 0 cnn)
% Maximal formula atoms : 25 ( 11 avg)
% Number of connectives : 619 ( 96 ~; 92 |; 66 &; 363 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 109 !; 0 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
factorial_plus_one: $i > $i ).
thf(func_def_2,type,
less: $i > $i > $o ).
thf(func_def_3,type,
prime: $i > $o ).
thf(func_def_4,type,
prime_divisor: $i > $i ).
thf(func_def_5,type,
divides: $i > $i > $o ).
thf(f1,conjecture,
~ ( ! [X1: $i,X0: $i] :
( ~ ( less @ X1 @ X0 )
| ~ ( less @ X0 @ X1 ) )
& ! [X2: $i,X1: $i,X0: $i] :
( ~ ( divides @ X1 @ X2 )
| ( divides @ X0 @ X2 )
| ~ ( divides @ X0 @ X1 ) )
& ! [X0: $i] :
( ( less @ ( prime_divisor @ X0 ) @ X0 )
| ( prime @ X0 ) )
& ! [X0: $i] :
( ( prime @ X0 )
| ( divides @ ( prime_divisor @ X0 ) @ X0 ) )
& ! [X0: $i] : ( divides @ X0 @ X0 )
& ! [X0: $i,X1: $i] :
( ~ ( divides @ X0 @ X1 )
| ~ ( less @ X1 @ X0 ) )
& ! [X0: $i] :
( ( less @ ( factorial_plus_one @ a ) @ X0 )
| ~ ( prime @ X0 )
| ~ ( less @ a @ X0 ) )
& ( prime @ a )
& ! [X0: $i] :
~ ( less @ X0 @ X0 )
& ! [X1: $i,X0: $i] :
( ~ ( divides @ X0 @ ( factorial_plus_one @ X1 ) )
| ( less @ X1 @ X0 ) )
& ! [X0: $i] : ( less @ X0 @ ( factorial_plus_one @ X0 ) )
& ! [X0: $i] :
( ( prime @ X0 )
| ( prime @ ( prime_divisor @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cNUM016_1) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X1: $i,X0: $i] :
( ~ ( less @ X1 @ X0 )
| ~ ( less @ X0 @ X1 ) )
& ! [X2: $i,X1: $i,X0: $i] :
( ~ ( divides @ X1 @ X2 )
| ( divides @ X0 @ X2 )
| ~ ( divides @ X0 @ X1 ) )
& ! [X0: $i] :
( ( less @ ( prime_divisor @ X0 ) @ X0 )
| ( prime @ X0 ) )
& ! [X0: $i] :
( ( prime @ X0 )
| ( divides @ ( prime_divisor @ X0 ) @ X0 ) )
& ! [X0: $i] : ( divides @ X0 @ X0 )
& ! [X0: $i,X1: $i] :
( ~ ( divides @ X0 @ X1 )
| ~ ( less @ X1 @ X0 ) )
& ! [X0: $i] :
( ( less @ ( factorial_plus_one @ a ) @ X0 )
| ~ ( prime @ X0 )
| ~ ( less @ a @ X0 ) )
& ( prime @ a )
& ! [X0: $i] :
~ ( less @ X0 @ X0 )
& ! [X1: $i,X0: $i] :
( ~ ( divides @ X0 @ ( factorial_plus_one @ X1 ) )
| ( less @ X1 @ X0 ) )
& ! [X0: $i] : ( less @ X0 @ ( factorial_plus_one @ X0 ) )
& ! [X0: $i] :
( ( prime @ X0 )
| ( prime @ ( prime_divisor @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( ~ ( less @ X0 @ X1 )
| ~ ( less @ X1 @ X0 ) )
& ! [X2: $i,X3: $i,X4: $i] :
( ~ ( divides @ X3 @ X2 )
| ( divides @ X4 @ X2 )
| ~ ( divides @ X4 @ X3 ) )
& ! [X5: $i] :
( ( less @ ( prime_divisor @ X5 ) @ X5 )
| ( prime @ X5 ) )
& ! [X6: $i] :
( ( prime @ X6 )
| ( divides @ ( prime_divisor @ X6 ) @ X6 ) )
& ! [X7: $i] : ( divides @ X7 @ X7 )
& ! [X8: $i,X9: $i] :
( ~ ( divides @ X8 @ X9 )
| ~ ( less @ X9 @ X8 ) )
& ! [X10: $i] :
( ( less @ ( factorial_plus_one @ a ) @ X10 )
| ~ ( prime @ X10 )
| ~ ( less @ a @ X10 ) )
& ( prime @ a )
& ! [X11: $i] :
~ ( less @ X11 @ X11 )
& ! [X12: $i,X13: $i] :
( ~ ( divides @ X13 @ ( factorial_plus_one @ X12 ) )
| ( less @ X12 @ X13 ) )
& ! [X14: $i] : ( less @ X14 @ ( factorial_plus_one @ X14 ) )
& ! [X15: $i] :
( ( prime @ X15 )
| ( prime @ ( prime_divisor @ X15 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( ( ( less @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
!= $true ) )
& ! [X2: $i,X3: $i,X4: $i] :
( ( ( divides @ X3 @ X2 )
!= $true )
| ( ( divides @ X4 @ X2 )
= $true )
| ( ( divides @ X4 @ X3 )
!= $true ) )
& ! [X5: $i] :
( ( $true
= ( prime @ X5 ) )
| ( $true
= ( less @ ( prime_divisor @ X5 ) @ X5 ) ) )
& ! [X6: $i] :
( ( $true
= ( divides @ ( prime_divisor @ X6 ) @ X6 ) )
| ( $true
= ( prime @ X6 ) ) )
& ! [X7: $i] :
( $true
= ( divides @ X7 @ X7 ) )
& ! [X8: $i,X9: $i] :
( ( $true
!= ( divides @ X8 @ X9 ) )
| ( $true
!= ( less @ X9 @ X8 ) ) )
& ! [X10: $i] :
( ( $true
= ( less @ ( factorial_plus_one @ a ) @ X10 ) )
| ( $true
!= ( prime @ X10 ) )
| ( $true
!= ( less @ a @ X10 ) ) )
& ( ( prime @ a )
= $true )
& ! [X11: $i] :
( $true
!= ( less @ X11 @ X11 ) )
& ! [X12: $i,X13: $i] :
( ( ( divides @ X13 @ ( factorial_plus_one @ X12 ) )
!= $true )
| ( ( less @ X12 @ X13 )
= $true ) )
& ! [X14: $i] :
( ( less @ X14 @ ( factorial_plus_one @ X14 ) )
= $true )
& ! [X15: $i] :
( ( $true
= ( prime @ X15 ) )
| ( $true
= ( prime @ ( prime_divisor @ X15 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i,X1: $i] :
( ( ( less @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
!= $true ) )
& ! [X7: $i] :
( $true
= ( divides @ X7 @ X7 ) )
& ! [X15: $i] :
( ( $true
= ( prime @ X15 ) )
| ( $true
= ( prime @ ( prime_divisor @ X15 ) ) ) )
& ! [X9: $i,X8: $i] :
( ( $true
!= ( less @ X9 @ X8 ) )
| ( $true
!= ( divides @ X8 @ X9 ) ) )
& ! [X12: $i,X13: $i] :
( ( ( divides @ X13 @ ( factorial_plus_one @ X12 ) )
!= $true )
| ( ( less @ X12 @ X13 )
= $true ) )
& ( ( prime @ a )
= $true )
& ! [X14: $i] :
( ( less @ X14 @ ( factorial_plus_one @ X14 ) )
= $true )
& ! [X11: $i] :
( $true
!= ( less @ X11 @ X11 ) )
& ! [X5: $i] :
( ( $true
= ( prime @ X5 ) )
| ( $true
= ( less @ ( prime_divisor @ X5 ) @ X5 ) ) )
& ! [X10: $i] :
( ( $true
!= ( prime @ X10 ) )
| ( $true
= ( less @ ( factorial_plus_one @ a ) @ X10 ) )
| ( $true
!= ( less @ a @ X10 ) ) )
& ! [X2: $i,X3: $i,X4: $i] :
( ( ( divides @ X4 @ X3 )
!= $true )
| ( ( divides @ X4 @ X2 )
= $true )
| ( ( divides @ X3 @ X2 )
!= $true ) )
& ! [X6: $i] :
( ( $true
= ( divides @ ( prime_divisor @ X6 ) @ X6 ) )
| ( $true
= ( prime @ X6 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( ( ( less @ X0 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
!= $true ) )
& ! [X2: $i] :
( $true
= ( divides @ X2 @ X2 ) )
& ! [X3: $i] :
( ( $true
= ( prime @ X3 ) )
| ( $true
= ( prime @ ( prime_divisor @ X3 ) ) ) )
& ! [X4: $i,X5: $i] :
( ( $true
!= ( less @ X4 @ X5 ) )
| ( $true
!= ( divides @ X5 @ X4 ) ) )
& ! [X6: $i,X7: $i] :
( ( $true
!= ( divides @ X7 @ ( factorial_plus_one @ X6 ) ) )
| ( $true
= ( less @ X6 @ X7 ) ) )
& ( ( prime @ a )
= $true )
& ! [X8: $i] :
( $true
= ( less @ X8 @ ( factorial_plus_one @ X8 ) ) )
& ! [X9: $i] :
( $true
!= ( less @ X9 @ X9 ) )
& ! [X10: $i] :
( ( $true
= ( prime @ X10 ) )
| ( $true
= ( less @ ( prime_divisor @ X10 ) @ X10 ) ) )
& ! [X11: $i] :
( ( $true
!= ( prime @ X11 ) )
| ( ( less @ ( factorial_plus_one @ a ) @ X11 )
= $true )
| ( $true
!= ( less @ a @ X11 ) ) )
& ! [X12: $i,X13: $i,X14: $i] :
( ( ( divides @ X14 @ X13 )
!= $true )
| ( $true
= ( divides @ X14 @ X12 ) )
| ( ( divides @ X13 @ X12 )
!= $true ) )
& ! [X15: $i] :
( ( ( divides @ ( prime_divisor @ X15 ) @ X15 )
= $true )
| ( $true
= ( prime @ X15 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
! [X15: $i] :
( ( ( divides @ ( prime_divisor @ X15 ) @ X15 )
= $true )
| ( $true
= ( prime @ X15 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X11: $i] :
( ( ( less @ ( factorial_plus_one @ a ) @ X11 )
= $true )
| ( $true
!= ( prime @ X11 ) )
| ( $true
!= ( less @ a @ X11 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
! [X9: $i] :
( $true
!= ( less @ X9 @ X9 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,plain,
! [X8: $i] :
( $true
= ( less @ X8 @ ( factorial_plus_one @ X8 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
! [X6: $i,X7: $i] :
( ( $true
!= ( divides @ X7 @ ( factorial_plus_one @ X6 ) ) )
| ( $true
= ( less @ X6 @ X7 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( divides @ X5 @ X4 ) )
| ( $true
!= ( less @ X4 @ X5 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f16,plain,
! [X3: $i] :
( ( $true
= ( prime @ ( prime_divisor @ X3 ) ) )
| ( $true
= ( prime @ X3 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f27,plain,
! [X0: $i] :
( ( ( less @ X0 @ ( prime_divisor @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( prime @ X0 )
= $true ) ),
inference(superposition,[],[f15,f7]) ).
thf(f28,plain,
! [X0: $i] :
( ( ( less @ X0 @ ( prime_divisor @ X0 ) )
!= $true )
| ( ( prime @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f30,plain,
! [X0: $i] :
( ( $true
= ( less @ X0 @ ( prime_divisor @ ( factorial_plus_one @ X0 ) ) ) )
| ( $true != $true )
| ( $true
= ( prime @ ( factorial_plus_one @ X0 ) ) ) ),
inference(superposition,[],[f14,f7]) ).
thf(f32,plain,
! [X0: $i] :
( ( $true
= ( less @ X0 @ ( prime_divisor @ ( factorial_plus_one @ X0 ) ) ) )
| ( $true
= ( prime @ ( factorial_plus_one @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f33,plain,
( ( $true != $true )
| ( $true
!= ( less @ a @ ( factorial_plus_one @ a ) ) )
| ( ( prime @ ( factorial_plus_one @ a ) )
!= $true ) ),
inference(superposition,[],[f11,f9]) ).
thf(f34,plain,
( ( $true
!= ( less @ a @ ( factorial_plus_one @ a ) ) )
| ( ( prime @ ( factorial_plus_one @ a ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
( ( prime @ ( factorial_plus_one @ a ) )
!= $true ),
inference(forward_subsumption_resolution,[],[f34,f12]) ).
thf(f37,definition,
( spl0_2
<=> ( ( prime @ ( factorial_plus_one @ a ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f39,plain,
( ( ( prime @ ( factorial_plus_one @ a ) )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f35,f37]) ).
thf(f45,plain,
( ( $true
!= ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) )
| ( $true != $true )
| ( $true
!= ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) )
| ( ( prime @ ( factorial_plus_one @ a ) )
= $true ) ),
inference(superposition,[],[f28,f9]) ).
thf(f46,plain,
( ( ( prime @ ( factorial_plus_one @ a ) )
= $true )
| ( $true
!= ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) )
| ( $true
!= ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f47,plain,
( ( $true
!= ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) )
| ( ( prime @ ( factorial_plus_one @ a ) )
= $true ) ),
inference(forward_subsumption_resolution,[],[f46,f16]) ).
thf(f49,definition,
( spl0_3
<=> ( $true
= ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f51,plain,
( ( $true
!= ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) )
| spl0_3 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f52,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f47,f49,f37]) ).
thf(f111,plain,
( ( ( prime @ ( factorial_plus_one @ a ) )
= $true )
| ( $true != $true )
| spl0_3 ),
inference(superposition,[],[f51,f32]) ).
thf(f112,plain,
( ( ( prime @ ( factorial_plus_one @ a ) )
= $true )
| spl0_3 ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f113,plain,
( $false
| spl0_2
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f112,f39]) ).
thf(f114,plain,
( spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f113]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f114]) ).
cnf(s5,plain,
spl0_3,
inference(rat,[],[s4,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s2]) ).
thf(f115,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 11:53:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.22 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
% 0.21/0.26 % (3049910)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.26 % (3049918)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=988391324:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.26 % (3049918) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3049910-3049918"...
% 0.21/0.26 % (3049918)...printing done.
% 0.21/0.26 % (3049918)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (3049918)------------------------------
% 0.21/0.26 % (3049918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (3049918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (3049918)CaDiCaL version: 2.1.3
% 0.21/0.26 % (3049918)Termination reason: Refutation
% 0.21/0.26 % (3049918)Time elapsed: 0.005 s
% 0.21/0.26 % (3049918)Peak memory usage: 13 MB
% 0.21/0.26 % (3049918)Instructions burned: 16 (million)
% 0.21/0.26 % (3049910)Success in time 0.028 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------