TSTP Solution File: NUM016^5 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 : Tue May 7 10:43:37 EDT 2024
% Result : Theorem 5.42s 2.42s
% Output : Refutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 8 unt; 6 typ; 0 def)
% Number of atoms : 198 ( 6 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 637 ( 90 ~; 89 |; 55 &; 403 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 0 ^ 114 !; 1 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $i ).
thf(factorial_plus_one_type,type,
factorial_plus_one: $i > $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(prime_type,type,
prime: $i > $o ).
thf(prime_divisor_type,type,
prime_divisor: $i > $i ).
thf(divides_type,type,
divides: $i > $i > $o ).
thf(1,conjecture,
~ ( ! [A: $i] :
~ ( less @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( divides @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ~ ( divides @ A @ B )
| ~ ( divides @ B @ C )
| ( divides @ A @ C ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) )
& ! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) )
& ( prime @ a )
& ! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cNUM016_1) ).
thf(2,negated_conjecture,
~ ~ ( ! [A: $i] :
~ ( less @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( divides @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ~ ( divides @ A @ B )
| ~ ( divides @ B @ C )
| ( divides @ A @ C ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) )
& ! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) )
& ( prime @ a )
& ! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ! [A: $i] :
~ ( less @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( divides @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ~ ( divides @ A @ B )
| ~ ( divides @ B @ C )
| ( divides @ A @ C ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) )
& ! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) )
& ( prime @ a )
& ! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ! [A: $i] :
~ ( less @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( divides @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ~ ( divides @ A @ B )
| ~ ( divides @ B @ C )
| ( divides @ A @ C ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) )
& ! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) )
& ( prime @ a )
& ! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ~ ? [A: $i] : ( less @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( divides @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ! [C: $i] :
( ~ ( divides @ B @ C )
| ( divides @ A @ C ) ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) )
& ! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) )
& ( prime @ a )
& ! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(13,plain,
! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(22,plain,
! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(11,plain,
! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(25,plain,
! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) ),
inference(simp,[status(thm)],[11]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( prime @ A )
| ( less @ C @ B )
| ( ( divides @ ( prime_divisor @ A ) @ A )
!= ( divides @ B @ ( factorial_plus_one @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,18]) ).
thf(62,plain,
! [A: $i] :
( ( prime @ ( factorial_plus_one @ A ) )
| ( less @ A @ ( prime_divisor @ ( factorial_plus_one @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( factorial_plus_one @ E )),bind(B,$thf( prime_divisor @ ( factorial_plus_one @ E ) )),bind(C,$thf( E ))]]) ).
thf(63,plain,
! [A: $i] :
( ( prime @ ( factorial_plus_one @ A ) )
| ( less @ A @ ( prime_divisor @ ( factorial_plus_one @ A ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(16,plain,
! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(24,plain,
! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( prime @ ( factorial_plus_one @ A ) )
| ~ ( prime @ B )
| ( less @ ( factorial_plus_one @ a ) @ B )
| ( ( less @ A @ ( prime_divisor @ ( factorial_plus_one @ A ) ) )
!= ( less @ a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[63,24]) ).
thf(188,plain,
( ( prime @ ( factorial_plus_one @ a ) )
| ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
| ( less @ ( factorial_plus_one @ a ) @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( a )),bind(B,$thf( prime_divisor @ ( factorial_plus_one @ a ) ))]]) ).
thf(7,plain,
! [A: $i] :
~ ( less @ A @ A ),
inference(cnf,[status(esa)],[5]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( ( less @ ( factorial_plus_one @ a ) @ A )
!= ( less @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[24,7]) ).
thf(171,plain,
( ~ ( prime @ ( factorial_plus_one @ a ) )
| ~ ( less @ a @ ( factorial_plus_one @ a ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( factorial_plus_one @ a )),bind(B,$thf( factorial_plus_one @ a ))]]) ).
thf(15,plain,
! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(27,plain,
! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) ),
inference(simp,[status(thm)],[15]) ).
thf(198,plain,
( ~ ( prime @ ( factorial_plus_one @ a ) )
| ~ $true ),
inference(rewrite,[status(thm)],[171,27]) ).
thf(199,plain,
~ ( prime @ ( factorial_plus_one @ a ) ),
inference(simp,[status(thm)],[198]) ).
thf(237,plain,
( $false
| ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
| ( less @ ( factorial_plus_one @ a ) @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ),
inference(rewrite,[status(thm)],[188,199]) ).
thf(238,plain,
( ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
| ( less @ ( factorial_plus_one @ a ) @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(9,plain,
! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(21,plain,
! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( prime @ A )
| ~ ( less @ C @ B )
| ( ( less @ ( prime_divisor @ A ) @ A )
!= ( less @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,20]) ).
thf(50,plain,
! [A: $i] :
( ( prime @ A )
| ~ ( less @ A @ ( prime_divisor @ A ) ) ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( D )),bind(B,$thf( prime_divisor @ D )),bind(C,$thf( D ))]]) ).
thf(57,plain,
! [A: $i] :
( ( prime @ A )
| ~ ( less @ A @ ( prime_divisor @ A ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(246,plain,
! [A: $i] :
( ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
| ( prime @ A )
| ( ( less @ ( factorial_plus_one @ a ) @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
!= ( less @ A @ ( prime_divisor @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,57]) ).
thf(247,plain,
( ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
| ( prime @ ( factorial_plus_one @ a ) ) ),
inference(pattern_uni,[status(thm)],[246:[bind(A,$thf( factorial_plus_one @ a ))]]) ).
thf(285,plain,
( ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
| $false ),
inference(rewrite,[status(thm)],[247,199]) ).
thf(286,plain,
~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(288,plain,
! [A: $i] :
( ( prime @ A )
| ( ( prime @ ( prime_divisor @ A ) )
!= ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,286]) ).
thf(289,plain,
prime @ ( factorial_plus_one @ a ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( factorial_plus_one @ a ))]]) ).
thf(291,plain,
$false,
inference(rewrite,[status(thm)],[289,199]) ).
thf(292,plain,
$false,
inference(simp,[status(thm)],[291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 6 19:27:54 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.91/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.05 % [INFO] Parsing done (150ms).
% 1.19/1.06 % [INFO] Running in sequential loop mode.
% 1.56/1.31 % [INFO] nitpick registered as external prover.
% 1.70/1.32 % [INFO] Scanning for conjecture ...
% 1.82/1.40 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 1.82/1.42 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.82/1.43 % [INFO] Problem is higher-order (TPTP THF).
% 1.82/1.43 % [INFO] Type checking passed.
% 1.82/1.43 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.42/2.41 % [INFO] Killing All external provers ...
% 5.42/2.42 % Time passed: 1962ms (effective reasoning time: 1351ms)
% 5.42/2.42 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.42/2.42 % Axioms used in derivation (0):
% 5.42/2.42 % No. of inferences in proof: 42
% 5.42/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1962 ms resp. 1351 ms w/o parsing
% 5.42/2.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.42/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------