%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM016^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:23:09 AM UTC 2026
% Result : Theorem 1.53s 1.26s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 421 ( 105 equ; 0 cnn)
% Maximal formula atoms : 25 ( 16 avg)
% Number of connectives : 585 ( 89 ~; 81 |; 66 &; 349 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 0 ^; 109 !; 0 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
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(f45,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f44,f10]) ).
thf(f10,plain,
! [X12: $i] :
( $true
= ( less @ X12 @ ( factorial_plus_one @ X12 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( less @ ( prime_divisor @ X0 ) @ X0 )
= $true )
| ( ( prime @ X0 )
= $true ) )
& ! [X1: $i,X2: $i] :
( ( ( less @ X2 @ X1 )
!= $true )
| ( ( less @ X1 @ X2 )
!= $true ) )
& ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( divides @ X3 @ X5 ) )
| ( $true
!= ( divides @ X5 @ X4 ) )
| ( ( divides @ X3 @ X4 )
= $true ) )
& ! [X6: $i] :
( ( less @ X6 @ X6 )
!= $true )
& ( ( prime @ a )
= $true )
& ! [X7: $i] :
( ( ( prime @ X7 )
= $true )
| ( ( divides @ ( prime_divisor @ X7 ) @ X7 )
= $true ) )
& ! [X8: $i] :
( ( ( less @ a @ X8 )
!= $true )
| ( ( prime @ X8 )
!= $true )
| ( ( less @ ( factorial_plus_one @ a ) @ X8 )
= $true ) )
& ! [X9: $i] :
( $true
= ( divides @ X9 @ X9 ) )
& ! [X10: $i,X11: $i] :
( ( ( less @ X10 @ X11 )
= $true )
| ( $true
!= ( divides @ X11 @ ( factorial_plus_one @ X10 ) ) ) )
& ! [X12: $i] :
( $true
= ( less @ X12 @ ( factorial_plus_one @ X12 ) ) )
& ! [X13: $i,X14: $i] :
( ( $true
!= ( less @ X14 @ X13 ) )
| ( $true
!= ( divides @ X13 @ X14 ) ) )
& ! [X15: $i] :
( ( ( prime @ X15 )
= $true )
| ( ( prime @ ( prime_divisor @ X15 ) )
= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X6: $i] :
( ( ( less @ ( prime_divisor @ X6 ) @ X6 )
= $true )
| ( ( prime @ X6 )
= $true ) )
& ! [X9: $i,X10: $i] :
( ( ( less @ X10 @ X9 )
!= $true )
| ( ( less @ X9 @ X10 )
!= $true ) )
& ! [X15: $i,X13: $i,X14: $i] :
( ( ( divides @ X15 @ X14 )
!= $true )
| ( $true
!= ( divides @ X14 @ X13 ) )
| ( ( divides @ X15 @ X13 )
= $true ) )
& ! [X7: $i] :
( $true
!= ( less @ X7 @ X7 ) )
& ( ( prime @ a )
= $true )
& ! [X8: $i] :
( ( ( prime @ X8 )
= $true )
| ( ( divides @ ( prime_divisor @ X8 ) @ X8 )
= $true ) )
& ! [X5: $i] :
( ( ( less @ a @ X5 )
!= $true )
| ( ( prime @ X5 )
!= $true )
| ( $true
= ( less @ ( factorial_plus_one @ a ) @ X5 ) ) )
& ! [X11: $i] :
( ( divides @ X11 @ X11 )
= $true )
& ! [X1: $i,X2: $i] :
( ( ( less @ X1 @ X2 )
= $true )
| ( ( divides @ X2 @ ( factorial_plus_one @ X1 ) )
!= $true ) )
& ! [X12: $i] :
( $true
= ( less @ X12 @ ( factorial_plus_one @ X12 ) ) )
& ! [X3: $i,X4: $i] :
( ( ( less @ X4 @ X3 )
!= $true )
| ( ( divides @ X3 @ X4 )
!= $true ) )
& ! [X0: $i] :
( ( ( prime @ X0 )
= $true )
| ( ( prime @ ( prime_divisor @ X0 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i] :
( ( ( prime @ X0 )
= $true )
| ( ( prime @ ( prime_divisor @ X0 ) )
= $true ) )
& ! [X1: $i,X2: $i] :
( ( ( less @ X1 @ X2 )
= $true )
| ( ( divides @ X2 @ ( factorial_plus_one @ X1 ) )
!= $true ) )
& ! [X3: $i,X4: $i] :
( ( ( less @ X4 @ X3 )
!= $true )
| ( ( divides @ X3 @ X4 )
!= $true ) )
& ! [X5: $i] :
( ( $true
= ( less @ ( factorial_plus_one @ a ) @ X5 ) )
| ( ( prime @ X5 )
!= $true )
| ( ( less @ a @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( ( less @ ( prime_divisor @ X6 ) @ X6 )
= $true )
| ( ( prime @ X6 )
= $true ) )
& ! [X7: $i] :
( $true
!= ( less @ X7 @ X7 ) )
& ! [X8: $i] :
( ( ( prime @ X8 )
= $true )
| ( ( divides @ ( prime_divisor @ X8 ) @ X8 )
= $true ) )
& ! [X9: $i,X10: $i] :
( ( ( less @ X10 @ X9 )
!= $true )
| ( ( less @ X9 @ X10 )
!= $true ) )
& ( ( prime @ a )
= $true )
& ! [X11: $i] :
( ( divides @ X11 @ X11 )
= $true )
& ! [X12: $i] :
( $true
= ( less @ X12 @ ( factorial_plus_one @ X12 ) ) )
& ! [X13: $i,X14: $i,X15: $i] :
( ( ( divides @ X15 @ X14 )
!= $true )
| ( ( divides @ X15 @ X13 )
= $true )
| ( $true
!= ( divides @ X14 @ X13 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i] :
( ( prime @ ( prime_divisor @ X0 ) )
| ( prime @ X0 ) )
& ! [X1: $i,X2: $i] :
( ( less @ X1 @ X2 )
| ~ ( divides @ X2 @ ( factorial_plus_one @ X1 ) ) )
& ! [X3: $i,X4: $i] :
( ~ ( less @ X4 @ X3 )
| ~ ( divides @ X3 @ X4 ) )
& ! [X5: $i] :
( ( less @ ( factorial_plus_one @ a ) @ X5 )
| ~ ( prime @ X5 )
| ~ ( less @ a @ X5 ) )
& ! [X6: $i] :
( ( prime @ X6 )
| ( less @ ( prime_divisor @ X6 ) @ X6 ) )
& ! [X7: $i] :
~ ( less @ X7 @ X7 )
& ! [X8: $i] :
( ( divides @ ( prime_divisor @ X8 ) @ X8 )
| ( prime @ X8 ) )
& ! [X9: $i,X10: $i] :
( ~ ( less @ X10 @ X9 )
| ~ ( less @ X9 @ X10 ) )
& ( prime @ a )
& ! [X11: $i] : ( divides @ X11 @ X11 )
& ! [X12: $i] : ( less @ X12 @ ( factorial_plus_one @ X12 ) )
& ! [X13: $i,X14: $i,X15: $i] :
( ~ ( divides @ X15 @ X14 )
| ( divides @ X15 @ X13 )
| ~ ( divides @ X14 @ X13 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X0: $i] :
( ( prime @ ( prime_divisor @ X0 ) )
| ( prime @ X0 ) )
& ! [X1: $i,X0: $i] :
( ( less @ X1 @ X0 )
| ~ ( divides @ X0 @ ( factorial_plus_one @ X1 ) ) )
& ! [X0: $i,X1: $i] :
( ~ ( less @ X1 @ X0 )
| ~ ( divides @ X0 @ X1 ) )
& ! [X0: $i] :
( ( less @ ( factorial_plus_one @ a ) @ X0 )
| ~ ( prime @ X0 )
| ~ ( less @ a @ X0 ) )
& ! [X0: $i] :
( ( prime @ X0 )
| ( less @ ( prime_divisor @ X0 ) @ X0 ) )
& ! [X0: $i] :
~ ( less @ X0 @ X0 )
& ! [X0: $i] :
( ( divides @ ( prime_divisor @ X0 ) @ X0 )
| ( prime @ X0 ) )
& ! [X1: $i,X0: $i] :
( ~ ( less @ X0 @ X1 )
| ~ ( less @ X1 @ X0 ) )
& ( prime @ a )
& ! [X0: $i] : ( divides @ X0 @ X0 )
& ! [X0: $i] : ( less @ X0 @ ( factorial_plus_one @ X0 ) )
& ! [X2: $i,X1: $i,X0: $i] :
( ~ ( divides @ X0 @ X1 )
| ( divides @ X0 @ X2 )
| ~ ( divides @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ! [X0: $i] :
( ( prime @ ( prime_divisor @ X0 ) )
| ( prime @ X0 ) )
& ! [X1: $i,X0: $i] :
( ( less @ X1 @ X0 )
| ~ ( divides @ X0 @ ( factorial_plus_one @ X1 ) ) )
& ! [X0: $i,X1: $i] :
( ~ ( less @ X1 @ X0 )
| ~ ( divides @ X0 @ X1 ) )
& ! [X0: $i] :
( ( less @ ( factorial_plus_one @ a ) @ X0 )
| ~ ( prime @ X0 )
| ~ ( less @ a @ X0 ) )
& ! [X0: $i] :
( ( prime @ X0 )
| ( less @ ( prime_divisor @ X0 ) @ X0 ) )
& ! [X0: $i] :
~ ( less @ X0 @ X0 )
& ! [X0: $i] :
( ( divides @ ( prime_divisor @ X0 ) @ X0 )
| ( prime @ X0 ) )
& ! [X1: $i,X0: $i] :
( ~ ( less @ X0 @ X1 )
| ~ ( less @ X1 @ X0 ) )
& ( prime @ a )
& ! [X0: $i] : ( divides @ X0 @ X0 )
& ! [X0: $i] : ( less @ X0 @ ( factorial_plus_one @ X0 ) )
& ! [X2: $i,X1: $i,X0: $i] :
( ~ ( divides @ X0 @ X1 )
| ( divides @ X0 @ X2 )
| ~ ( divides @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3tQOHq4VEF/DTF2THF_512.p',cNUM016_1) ).
thf(f44,plain,
( ( less @ a @ ( factorial_plus_one @ a ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f38,f43]) ).
thf(f43,plain,
( $true
= ( prime @ ( factorial_plus_one @ a ) ) ),
inference(subsumption_resolution,[status(thm)],[f42,f8]) ).
thf(f8,plain,
! [X15: $i] :
( ( ( prime @ ( prime_divisor @ X15 ) )
= $true )
| ( ( prime @ X15 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f42,plain,
( ( $true
= ( prime @ ( factorial_plus_one @ a ) ) )
| ( $true
!= ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f40,f31]) ).
thf(f31,plain,
! [X0: $i] :
( ( ( less @ X0 @ ( prime_divisor @ ( factorial_plus_one @ X0 ) ) )
= $true )
| ( ( prime @ ( factorial_plus_one @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i] :
( ( ( less @ X0 @ ( prime_divisor @ ( factorial_plus_one @ X0 ) ) )
= $true )
| ( ( prime @ ( factorial_plus_one @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f14]) ).
thf(f14,plain,
! [X7: $i] :
( ( ( divides @ ( prime_divisor @ X7 ) @ X7 )
= $true )
| ( ( prime @ X7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f11,plain,
! [X10: $i,X11: $i] :
( ( $true
!= ( divides @ X11 @ ( factorial_plus_one @ X10 ) ) )
| ( ( less @ X10 @ X11 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f40,plain,
( ( ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
!= $true )
| ( $true
= ( prime @ ( factorial_plus_one @ a ) ) )
| ( $true
!= ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true != $true )
| ( $true
= ( prime @ ( factorial_plus_one @ a ) ) )
| ( $true
!= ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) )
| ( ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f23,f13]) ).
thf(f13,plain,
! [X8: $i] :
( ( ( less @ ( factorial_plus_one @ a ) @ X8 )
= $true )
| ( ( prime @ X8 )
!= $true )
| ( ( less @ a @ X8 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f23,plain,
! [X0: $i] :
( ( $true
!= ( less @ X0 @ ( prime_divisor @ X0 ) ) )
| ( ( prime @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( less @ X0 @ ( prime_divisor @ X0 ) ) )
| ( ( prime @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f9,f14]) ).
thf(f9,plain,
! [X14: $i,X13: $i] :
( ( $true
!= ( divides @ X13 @ X14 ) )
| ( $true
!= ( less @ X14 @ X13 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f38,plain,
( ( $true
!= ( prime @ ( factorial_plus_one @ a ) ) )
| ( ( less @ a @ ( factorial_plus_one @ a ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true != $true )
| ( $true
!= ( prime @ ( factorial_plus_one @ a ) ) )
| ( ( less @ a @ ( factorial_plus_one @ a ) )
!= $true ) ),
inference(superposition,[status(thm)],[f16,f13]) ).
thf(f16,plain,
! [X6: $i] :
( ( less @ X6 @ X6 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM016^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 10:54:55 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : NUM016^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.44 % Domain : Number Theory
% 0.19/0.44 % Problem : TPS problem NUM016-1
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English : There exist infinitely many primes.
% 0.19/0.44
% 0.19/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Bro09]
% 0.19/0.44 % Names : tps_0442 [Bro09]
% 0.19/0.44 % : NUM016-1 [TPS]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.17 v9.1.0, 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.19/0.44 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.19/0.44 % Number of atoms : 22 ( 0 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 22 ( 22 avg)
% 0.19/0.44 % Number of connectives : 76 ( 11 ~; 10 |; 11 &; 44 @)
% 0.19/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 19 ( 19 avg)
% 0.19/0.44 % Number of types : 2 ( 0 usr)
% 0.19/0.44 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 6 ( 6 usr; 1 con; 0-2 aty)
% 0.19/0.44 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 0.19/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.44 % :
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(a,type,
% 0.19/0.44 a: $i ).
% 0.19/0.44
% 0.19/0.44 thf(factorial_plus_one,type,
% 0.19/0.44 factorial_plus_one: $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(less,type,
% 0.19/0.44 less: $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(prime,type,
% 0.19/0.44 prime: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(prime_divisor,type,
% 0.19/0.44 prime_divisor: $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(divides,type,
% 0.19/0.44 divides: $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(cNUM016_1,conjecture,
% 0.19/0.44 ~ ( ! [X: $i] :
% 0.19/0.44 ~ ( less @ X @ X )
% 0.19/0.44 & ! [X: $i,Y: $i] :
% 0.19/0.44 ( ~ ( less @ X @ Y )
% 0.19/0.44 | ~ ( less @ Y @ X ) )
% 0.19/0.44 & ! [X: $i] : ( divides @ X @ X )
% 0.19/0.44 & ! [X: $i,Y: $i,Z: $i] :
% 0.19/0.44 ( ~ ( divides @ X @ Y )
% 0.19/0.44 | ~ ( divides @ Y @ Z )
% 0.19/0.44 | ( divides @ X @ Z ) )
% 0.19/0.44 & ! [X: $i,Y: $i] :
% 0.19/0.44 ( ~ ( divides @ X @ Y )
% 0.19/0.44 | ~ ( less @ Y @ X ) )
% 0.19/0.44 & ! [X: $i] : ( less @ X @ ( factorial_plus_one @ X ) )
% 0.19/0.44 & ! [X: $i,Y: $i] :
% 0.19/0.44 ( ~ ( divides @ X @ ( factorial_plus_one @ Y ) )
% 0.19/0.44 | ( less @ Y @ X ) )
% 0.19/0.44 & ! [X: $i] :
% 0.19/0.44 ( ( prime @ X )
% 0.19/0.44 | ( divides @ ( prime_divisor @ X ) @ X ) )
% 0.19/0.44 & ! [X: $i] :
% 0.19/0.44 ( ( prime @ X )
% 0.19/0.44 | ( prime @ ( prime_divisor @ X ) ) )
% 0.19/0.44 & ! [X: $i] :
% 0.19/0.44 ( ( prime @ X )
% 0.19/0.44 | ( less @ ( prime_divisor @ X ) @ X ) )
% 0.19/0.44 & ( prime @ a )
% 0.19/0.44 & ! [X: $i] :
% 0.19/0.44 ( ~ ( prime @ X )
% 0.19/0.44 | ~ ( less @ a @ X )
% 0.19/0.44 | ( less @ ( factorial_plus_one @ a ) @ X ) ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.53/1.23 ---- Embedded in THF ---
% 1.53/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.23 %%% Generated on Tue Feb 24 10:54:56 EST 2026
% 1.53/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.23 %%% Logic specification used:
% 1.53/1.23 %%% thf(spec, logic, $$dhol).
% 1.53/1.23
% 1.53/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3tQOHq4VEF/DTF2DTF512.p
% See solution above
% 1.53/1.23 ------------------------
% 1.53/1.24 ---- Cleaned THF ---
% 1.53/1.24 thf(a,type,
% 1.53/1.24 a: $i ).
% 1.53/1.24
% 1.53/1.24 thf(factorial_plus_one,type,
% 1.53/1.24 factorial_plus_one: $i > $i ).
% 1.53/1.24
% 1.53/1.24 thf(less,type,
% 1.53/1.24 less: $i > $i > $o ).
% 1.53/1.24
% 1.53/1.24 thf(prime,type,
% 1.53/1.24 prime: $i > $o ).
% 1.53/1.24
% 1.53/1.24 thf(prime_divisor,type,
% 1.53/1.24 prime_divisor: $i > $i ).
% 1.53/1.24
% 1.53/1.24 thf(divides,type,
% 1.53/1.24 divides: $i > $i > $o ).
% 1.53/1.24
% 1.53/1.24 thf(cNUM016_1,conjecture,
% 1.53/1.24 ~ ( ! [X: $i] :
% 1.53/1.24 ~ ( less @ X @ X )
% 1.53/1.24 & ! [X: $i,Y: $i] :
% 1.53/1.24 ( ~ ( less @ X @ Y )
% 1.53/1.24 | ~ ( less @ Y @ X ) )
% 1.53/1.24 & ! [X: $i] : ( divides @ X @ X )
% 1.53/1.24 & ! [X: $i,Y: $i,Z: $i] :
% 1.53/1.24 ( ~ ( divides @ X @ Y )
% 1.53/1.24 | ~ ( divides @ Y @ Z )
% 1.53/1.24 | ( divides @ X @ Z ) )
% 1.53/1.24 & ! [X: $i,Y: $i] :
% 1.53/1.24 ( ~ ( divides @ X @ Y )
% 1.53/1.24 | ~ ( less @ Y @ X ) )
% 1.53/1.24 & ! [X: $i] : ( less @ X @ ( factorial_plus_one @ X ) )
% 1.53/1.24 & ! [X: $i,Y: $i] :
% 1.53/1.24 ( ~ ( divides @ X @ ( factorial_plus_one @ Y ) )
% 1.53/1.24 | ( less @ Y @ X ) )
% 1.53/1.24 & ! [X: $i] :
% 1.53/1.24 ( ( prime @ X )
% 1.53/1.24 | ( divides @ ( prime_divisor @ X ) @ X ) )
% 1.53/1.24 & ! [X: $i] :
% 1.53/1.24 ( ( prime @ X )
% 1.53/1.24 | ( prime @ ( prime_divisor @ X ) ) )
% 1.53/1.24 & ! [X: $i] :
% 1.53/1.24 ( ( prime @ X )
% 1.53/1.24 | ( less @ ( prime_divisor @ X ) @ X ) )
% 1.53/1.24 & ( prime @ a )
% 1.53/1.24 & ! [X: $i] :
% 1.53/1.24 ( ~ ( prime @ X )
% 1.53/1.24 | ~ ( less @ a @ X )
% 1.53/1.24 | ( less @ ( factorial_plus_one @ a ) @ X ) ) ) ).
% 1.53/1.24 ------------------------
% 1.53/1.25 % (833)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_512 for (2999ds/183Mi)
% 1.53/1.25 % (834)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_512 for (2999ds/4Mi)
% 1.53/1.25 % (836)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_512 for (2999ds/2Mi)
% 1.53/1.25 % (834)Instruction limit reached!
% 1.53/1.25 % (834)------------------------------
% 1.53/1.25 % (834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (834)Termination reason: Unknown
% 1.53/1.25 % (834)Termination phase: Saturation
% 1.53/1.25
% 1.53/1.25 % (834)Memory used [KB]: 5500
% 1.53/1.25 % (834)Time elapsed: 0.003 s
% 1.53/1.25 % (834)Instructions burned: 5 (million)
% 1.53/1.25 % (834)------------------------------
% 1.53/1.25 % (834)------------------------------
% 1.53/1.25 % (836)Instruction limit reached!
% 1.53/1.25 % (836)------------------------------
% 1.53/1.25 % (836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (836)Termination reason: Unknown
% 1.53/1.25 % (836)Termination phase: Saturation
% 1.53/1.25
% 1.53/1.25 % (836)Memory used [KB]: 5500
% 1.53/1.25 % (836)Time elapsed: 0.002 s
% 1.53/1.25 % (836)Instructions burned: 3 (million)
% 1.53/1.25 % (836)------------------------------
% 1.53/1.25 % (836)------------------------------
% 1.53/1.26 % (833)First to succeed.
% 1.53/1.26 % (833)Refutation found. Thanks to Tanya!
% 1.53/1.26 % SZS status Theorem for DTF2THF_512
% 1.53/1.26 % SZS output start Proof for DTF2THF_512
% 1.53/1.26 thf(func_def_1, type, factorial_plus_one: $i > $i).
% 1.53/1.26 thf(func_def_2, type, less: $i > $i > $o).
% 1.53/1.26 thf(func_def_3, type, prime: $i > $o).
% 1.53/1.26 thf(func_def_4, type, prime_divisor: $i > $i).
% 1.53/1.26 thf(func_def_5, type, divides: $i > $i > $o).
% 1.53/1.26 thf(f45,plain,(
% 1.53/1.26 $false),
% 1.53/1.26 inference(subsumption_resolution,[status(thm)],[f44,f10])).
% 1.53/1.26 thf(f10,plain,(
% 1.53/1.26 ( ! [X12 : $i] : (($true = (less @ X12 @ (factorial_plus_one @ X12)))) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.26 thf(f7,plain,(
% 1.53/1.26 ! [X0 : $i] : (((less @ (prime_divisor @ X0) @ X0) = $true) | ((prime @ X0) = $true)) & ! [X1 : $i,X2 : $i] : (((less @ X2 @ X1) != $true) | ((less @ X1 @ X2) != $true)) & ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (divides @ X3 @ X5)) | ($true != (divides @ X5 @ X4)) | ((divides @ X3 @ X4) = $true)) & ! [X6 : $i] : ((less @ X6 @ X6) != $true) & ((prime @ a) = $true) & ! [X7 : $i] : (((prime @ X7) = $true) | ((divides @ (prime_divisor @ X7) @ X7) = $true)) & ! [X8 : $i] : (((less @ a @ X8) != $true) | ((prime @ X8) != $true) | ((less @ (factorial_plus_one @ a) @ X8) = $true)) & ! [X9 : $i] : ($true = (divides @ X9 @ X9)) & ! [X10 : $i,X11 : $i] : (((less @ X10 @ X11) = $true) | ($true != (divides @ X11 @ (factorial_plus_one @ X10)))) & ! [X12 : $i] : ($true = (less @ X12 @ (factorial_plus_one @ X12))) & ! [X13 : $i,X14 : $i] : (($true != (less @ X14 @ X13)) | ($true != (divides @ X13 @ X14))) & ! [X15 : $i] : (((prime @ X15) = $true) | ((prime @ (prime_divisor @ X15)) = $true))),
% 1.53/1.26 inference(rectify,[status(thm)],[f6])).
% 1.53/1.26 thf(f6,plain,(
% 1.53/1.26 ! [X6 : $i] : (((less @ (prime_divisor @ X6) @ X6) = $true) | ((prime @ X6) = $true)) & ! [X9 : $i,X10 : $i] : (((less @ X10 @ X9) != $true) | ((less @ X9 @ X10) != $true)) & ! [X15 : $i,X13 : $i,X14 : $i] : (((divides @ X15 @ X14) != $true) | ($true != (divides @ X14 @ X13)) | ((divides @ X15 @ X13) = $true)) & ! [X7 : $i] : ($true != (less @ X7 @ X7)) & ((prime @ a) = $true) & ! [X8 : $i] : (((prime @ X8) = $true) | ((divides @ (prime_divisor @ X8) @ X8) = $true)) & ! [X5 : $i] : (((less @ a @ X5) != $true) | ((prime @ X5) != $true) | ($true = (less @ (factorial_plus_one @ a) @ X5))) & ! [X11 : $i] : ((divides @ X11 @ X11) = $true) & ! [X1 : $i,X2 : $i] : (((less @ X1 @ X2) = $true) | ((divides @ X2 @ (factorial_plus_one @ X1)) != $true)) & ! [X12 : $i] : ($true = (less @ X12 @ (factorial_plus_one @ X12))) & ! [X3 : $i,X4 : $i] : (((less @ X4 @ X3) != $true) | ((divides @ X3 @ X4) != $true)) & ! [X0 : $i] : (((prime @ X0) = $true) | ((prime @ (prime_divisor @ X0)) = $true))),
% 1.53/1.26 inference(flattening,[status(thm)],[f5])).
% 1.53/1.26 thf(f5,plain,(
% 1.53/1.26 ~~(! [X0 : $i] : (((prime @ X0) = $true) | ((prime @ (prime_divisor @ X0)) = $true)) & ! [X1 : $i,X2 : $i] : (((less @ X1 @ X2) = $true) | ~((divides @ X2 @ (factorial_plus_one @ X1)) = $true)) & ! [X3 : $i,X4 : $i] : (~((less @ X4 @ X3) = $true) | ~((divides @ X3 @ X4) = $true)) & ! [X5 : $i] : (($true = (less @ (factorial_plus_one @ a) @ X5)) | ~((prime @ X5) = $true) | ~((less @ a @ X5) = $true)) & ! [X6 : $i] : (((less @ (prime_divisor @ X6) @ X6) = $true) | ((prime @ X6) = $true)) & ! [X7 : $i] : ~($true = (less @ X7 @ X7)) & ! [X8 : $i] : (((prime @ X8) = $true) | ((divides @ (prime_divisor @ X8) @ X8) = $true)) & ! [X9 : $i,X10 : $i] : (~((less @ X10 @ X9) = $true) | ~((less @ X9 @ X10) = $true)) & ((prime @ a) = $true) & ! [X11 : $i] : ((divides @ X11 @ X11) = $true) & ! [X12 : $i] : ($true = (less @ X12 @ (factorial_plus_one @ X12))) & ! [X13 : $i,X14 : $i,X15 : $i] : (~((divides @ X15 @ X14) = $true) | ((divides @ X15 @ X13) = $true) | ~($true = (divides @ X14 @ X13))))),
% 1.53/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.26 thf(f4,plain,(
% 1.53/1.26 ~~(! [X0 : $i] : ((prime @ (prime_divisor @ X0)) | (prime @ X0)) & ! [X1 : $i,X2 : $i] : ((less @ X1 @ X2) | ~(divides @ X2 @ (factorial_plus_one @ X1))) & ! [X3 : $i,X4 : $i] : (~(less @ X4 @ X3) | ~(divides @ X3 @ X4)) & ! [X5 : $i] : ((less @ (factorial_plus_one @ a) @ X5) | ~(prime @ X5) | ~(less @ a @ X5)) & ! [X6 : $i] : ((prime @ X6) | (less @ (prime_divisor @ X6) @ X6)) & ! [X7 : $i] : ~(less @ X7 @ X7) & ! [X8 : $i] : ((divides @ (prime_divisor @ X8) @ X8) | (prime @ X8)) & ! [X9 : $i,X10 : $i] : (~(less @ X10 @ X9) | ~(less @ X9 @ X10)) & (prime @ a) & ! [X11 : $i] : (divides @ X11 @ X11) & ! [X12 : $i] : (less @ X12 @ (factorial_plus_one @ X12)) & ! [X13 : $i,X14 : $i,X15 : $i] : (~(divides @ X15 @ X14) | (divides @ X15 @ X13) | ~(divides @ X14 @ X13)))),
% 1.53/1.26 inference(rectify,[status(thm)],[f2])).
% 1.53/1.26 thf(f2,negated_conjecture,(
% 1.53/1.26 ~~(! [X0 : $i] : ((prime @ (prime_divisor @ X0)) | (prime @ X0)) & ! [X1 : $i,X0 : $i] : ((less @ X1 @ X0) | ~(divides @ X0 @ (factorial_plus_one @ X1))) & ! [X0 : $i,X1 : $i] : (~(less @ X1 @ X0) | ~(divides @ X0 @ X1)) & ! [X0 : $i] : ((less @ (factorial_plus_one @ a) @ X0) | ~(prime @ X0) | ~(less @ a @ X0)) & ! [X0 : $i] : ((prime @ X0) | (less @ (prime_divisor @ X0) @ X0)) & ! [X0 : $i] : ~(less @ X0 @ X0) & ! [X0 : $i] : ((divides @ (prime_divisor @ X0) @ X0) | (prime @ X0)) & ! [X1 : $i,X0 : $i] : (~(less @ X0 @ X1) | ~(less @ X1 @ X0)) & (prime @ a) & ! [X0 : $i] : (divides @ X0 @ X0) & ! [X0 : $i] : (less @ X0 @ (factorial_plus_one @ X0)) & ! [X2 : $i,X1 : $i,X0 : $i] : (~(divides @ X0 @ X1) | (divides @ X0 @ X2) | ~(divides @ X1 @ X2)))),
% 1.53/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.26 thf(f1,conjecture,(
% 1.53/1.26 ~(! [X0 : $i] : ((prime @ (prime_divisor @ X0)) | (prime @ X0)) & ! [X1 : $i,X0 : $i] : ((less @ X1 @ X0) | ~(divides @ X0 @ (factorial_plus_one @ X1))) & ! [X0 : $i,X1 : $i] : (~(less @ X1 @ X0) | ~(divides @ X0 @ X1)) & ! [X0 : $i] : ((less @ (factorial_plus_one @ a) @ X0) | ~(prime @ X0) | ~(less @ a @ X0)) & ! [X0 : $i] : ((prime @ X0) | (less @ (prime_divisor @ X0) @ X0)) & ! [X0 : $i] : ~(less @ X0 @ X0) & ! [X0 : $i] : ((divides @ (prime_divisor @ X0) @ X0) | (prime @ X0)) & ! [X1 : $i,X0 : $i] : (~(less @ X0 @ X1) | ~(less @ X1 @ X0)) & (prime @ a) & ! [X0 : $i] : (divides @ X0 @ X0) & ! [X0 : $i] : (less @ X0 @ (factorial_plus_one @ X0)) & ! [X2 : $i,X1 : $i,X0 : $i] : (~(divides @ X0 @ X1) | (divides @ X0 @ X2) | ~(divides @ X1 @ X2)))),
% 1.53/1.26 file('/export/starexec/sandbox/tmp/tmp.3tQOHq4VEF/DTF2THF_512.p',cNUM016_1)).
% 1.53/1.26 thf(f44,plain,(
% 1.53/1.26 ((less @ a @ (factorial_plus_one @ a)) != $true)),
% 1.53/1.26 inference(subsumption_resolution,[status(thm)],[f38,f43])).
% 1.53/1.26 thf(f43,plain,(
% 1.53/1.26 ($true = (prime @ (factorial_plus_one @ a)))),
% 1.53/1.26 inference(subsumption_resolution,[status(thm)],[f42,f8])).
% 1.53/1.26 thf(f8,plain,(
% 1.53/1.26 ( ! [X15 : $i] : (((prime @ (prime_divisor @ X15)) = $true) | ((prime @ X15) = $true)) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.26 thf(f42,plain,(
% 1.53/1.26 ($true = (prime @ (factorial_plus_one @ a))) | ($true != (prime @ (prime_divisor @ (factorial_plus_one @ a))))),
% 1.53/1.26 inference(subsumption_resolution,[status(thm)],[f40,f31])).
% 1.53/1.26 thf(f31,plain,(
% 1.53/1.26 ( ! [X0 : $i] : (((less @ X0 @ (prime_divisor @ (factorial_plus_one @ X0))) = $true) | ((prime @ (factorial_plus_one @ X0)) = $true)) )),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.53/1.26 thf(f29,plain,(
% 1.53/1.26 ( ! [X0 : $i] : (((less @ X0 @ (prime_divisor @ (factorial_plus_one @ X0))) = $true) | ((prime @ (factorial_plus_one @ X0)) = $true) | ($true != $true)) )),
% 1.53/1.26 inference(superposition,[status(thm)],[f11,f14])).
% 1.53/1.26 thf(f14,plain,(
% 1.53/1.26 ( ! [X7 : $i] : (((divides @ (prime_divisor @ X7) @ X7) = $true) | ((prime @ X7) = $true)) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.26 thf(f11,plain,(
% 1.53/1.26 ( ! [X10 : $i,X11 : $i] : (($true != (divides @ X11 @ (factorial_plus_one @ X10))) | ((less @ X10 @ X11) = $true)) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.26 thf(f40,plain,(
% 1.53/1.26 ((less @ a @ (prime_divisor @ (factorial_plus_one @ a))) != $true) | ($true = (prime @ (factorial_plus_one @ a))) | ($true != (prime @ (prime_divisor @ (factorial_plus_one @ a))))),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.53/1.26 thf(f36,plain,(
% 1.53/1.26 ($true != $true) | ($true = (prime @ (factorial_plus_one @ a))) | ($true != (prime @ (prime_divisor @ (factorial_plus_one @ a)))) | ((less @ a @ (prime_divisor @ (factorial_plus_one @ a))) != $true)),
% 1.53/1.26 inference(superposition,[status(thm)],[f23,f13])).
% 1.53/1.26 thf(f13,plain,(
% 1.53/1.26 ( ! [X8 : $i] : (((less @ (factorial_plus_one @ a) @ X8) = $true) | ((prime @ X8) != $true) | ((less @ a @ X8) != $true)) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.26 thf(f23,plain,(
% 1.53/1.26 ( ! [X0 : $i] : (($true != (less @ X0 @ (prime_divisor @ X0))) | ((prime @ X0) = $true)) )),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.53/1.26 thf(f21,plain,(
% 1.53/1.26 ( ! [X0 : $i] : (($true != $true) | ($true != (less @ X0 @ (prime_divisor @ X0))) | ((prime @ X0) = $true)) )),
% 1.53/1.26 inference(superposition,[status(thm)],[f9,f14])).
% 1.53/1.26 thf(f9,plain,(
% 1.53/1.26 ( ! [X14 : $i,X13 : $i] : (($true != (divides @ X13 @ X14)) | ($true != (less @ X14 @ X13))) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.26 thf(f38,plain,(
% 1.53/1.26 ($true != (prime @ (factorial_plus_one @ a))) | ((less @ a @ (factorial_plus_one @ a)) != $true)),
% 1.53/1.26 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.53/1.26 thf(f35,plain,(
% 1.53/1.26 ($true != $true) | ($true != (prime @ (factorial_plus_one @ a))) | ((less @ a @ (factorial_plus_one @ a)) != $true)),
% 1.53/1.26 inference(superposition,[status(thm)],[f16,f13])).
% 1.53/1.26 thf(f16,plain,(
% 1.53/1.26 ( ! [X6 : $i] : (((less @ X6 @ X6) != $true)) )),
% 1.53/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.26 % SZS output end Proof for DTF2THF_512
% 1.53/1.26 % (833)------------------------------
% 1.53/1.26 % (833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.26 % (833)Termination reason: Refutation
% 1.53/1.26
% 1.53/1.26 % (833)Memory used [KB]: 5628
% 1.53/1.26 % (833)Time elapsed: 0.005 s
% 1.53/1.26 % (833)Instructions burned: 6 (million)
% 1.53/1.26 % (833)------------------------------
% 1.53/1.26 % (833)------------------------------
% 1.53/1.26 % (832)Success in time 0.015 s
%------------------------------------------------------------------------------