TSTP Solution File: FLD012-4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : FLD012-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Fri May 19 11:07:43 EDT 2023
% Result : Unsatisfiable 5.37s 2.22s
% Output : Refutation 5.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 49
% Syntax : Number of formulae : 85 ( 25 unt; 14 typ; 0 def)
% Number of atoms : 173 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 624 ( 104 ~; 102 |; 0 &; 418 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 146 ( 0 ^; 146 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(u_type,type,
u: $i ).
thf(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $i ).
thf(v_type,type,
v: $i ).
thf(multiplicative_identity_type,type,
multiplicative_identity: $i ).
thf(less_or_equal_type,type,
less_or_equal: $i > $i > $o ).
thf(defined_type,type,
defined: $i > $o ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(20,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( sum @ D @ E @ A )
| ~ ( product @ D @ B @ F )
| ~ ( product @ E @ B @ G )
| ~ ( sum @ F @ G @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_2) ).
thf(69,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( sum @ D @ E @ A )
| ~ ( product @ D @ B @ F )
| ~ ( product @ E @ B @ G )
| ~ ( sum @ F @ G @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
defined @ multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(56,plain,
defined @ multiplicative_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
~ ( sum @ additive_identity @ a @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
thf(37,plain,
~ ( sum @ additive_identity @ a @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( defined @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( defined @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
~ ( sum @ additive_identity @ b @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_6) ).
thf(38,plain,
~ ( sum @ additive_identity @ b @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i] :
( ( sum @ ( additive_inverse @ A ) @ A @ additive_identity )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(65,plain,
! [A: $i] :
( ( sum @ ( additive_inverse @ A ) @ A @ additive_identity )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
defined @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
thf(73,plain,
defined @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ A @ C )
| ~ ( less_or_equal @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ A @ C )
| ~ ( less_or_equal @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,axiom,
~ ( sum @ additive_identity @ additive_identity @ multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
thf(91,plain,
~ ( sum @ additive_identity @ additive_identity @ multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(30,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ D @ E @ F )
| ~ ( product @ F @ G @ C )
| ~ ( product @ D @ G @ A )
| ~ ( product @ E @ G @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_1) ).
thf(87,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ D @ E @ F )
| ~ ( product @ F @ G @ C )
| ~ ( product @ D @ G @ A )
| ~ ( product @ E @ G @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,negated_conjecture,
product @ ( multiplicative_inverse @ a ) @ ( multiplicative_inverse @ b ) @ v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_8) ).
thf(40,plain,
product @ ( multiplicative_inverse @ a ) @ ( multiplicative_inverse @ b ) @ v,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,negated_conjecture,
~ ( product @ multiplicative_identity @ ( multiplicative_inverse @ u ) @ v ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_9) ).
thf(36,plain,
~ ( product @ multiplicative_identity @ ( multiplicative_inverse @ u ) @ v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( product @ D @ F @ B )
| ~ ( product @ E @ F @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication_1) ).
thf(79,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( product @ D @ F @ B )
| ~ ( product @ E @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(16,axiom,
defined @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
thf(62,plain,
defined @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
! [A: $i] :
( ( product @ ( multiplicative_inverse @ A ) @ A @ multiplicative_identity )
| ( sum @ additive_identity @ A @ additive_identity )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(83,plain,
! [A: $i] :
( ( product @ ( multiplicative_inverse @ A ) @ A @ multiplicative_identity )
| ( sum @ additive_identity @ A @ additive_identity )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
! [A: $i] :
( ( defined @ ( additive_inverse @ A ) )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(46,plain,
! [A: $i] :
( ( defined @ ( additive_inverse @ A ) )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ C @ D )
| ~ ( sum @ C @ E @ A )
| ~ ( sum @ D @ E @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(93,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ C @ D )
| ~ ( sum @ C @ E @ A )
| ~ ( sum @ D @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,axiom,
defined @ v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_is_defined) ).
thf(57,plain,
defined @ v,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
defined @ additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(74,plain,
defined @ additive_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
! [A: $i] :
( ( defined @ ( multiplicative_inverse @ A ) )
| ~ ( defined @ A )
| ( sum @ additive_identity @ A @ additive_identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(60,plain,
! [A: $i] :
( ( defined @ ( multiplicative_inverse @ A ) )
| ~ ( defined @ A )
| ( sum @ additive_identity @ A @ additive_identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( sum @ A @ B @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_addition) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( sum @ A @ B @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(35,axiom,
! [A: $i] :
( ( sum @ additive_identity @ A @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(96,plain,
! [A: $i] :
( ( sum @ additive_identity @ A @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ additive_identity @ A )
| ~ ( less_or_equal @ additive_identity @ B )
| ~ ( less_or_equal @ additive_identity @ C )
| ~ ( product @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ additive_identity @ A )
| ~ ( less_or_equal @ additive_identity @ B )
| ~ ( less_or_equal @ additive_identity @ C )
| ~ ( product @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ D @ E @ A )
| ~ ( sum @ E @ B @ F )
| ~ ( sum @ D @ F @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_2) ).
thf(54,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ D @ E @ A )
| ~ ( sum @ E @ B @ F )
| ~ ( sum @ D @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [A: $i] :
( ( product @ multiplicative_identity @ A @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(81,plain,
! [A: $i] :
( ( product @ multiplicative_identity @ A @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,negated_conjecture,
product @ a @ b @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).
thf(39,plain,
product @ a @ b @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ( less_or_equal @ B @ A )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ( less_or_equal @ B @ A )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ D @ E @ A )
| ~ ( product @ E @ B @ F )
| ~ ( product @ D @ F @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication_2) ).
thf(63,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ D @ E @ A )
| ~ ( product @ E @ B @ F )
| ~ ( product @ D @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(34,axiom,
defined @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
thf(95,plain,
defined @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( defined @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( defined @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( product @ A @ B @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_multiplication) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( product @ A @ B @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( sum @ additive_identity @ A @ B )
| ~ ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( sum @ additive_identity @ A @ B )
| ~ ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ A @ D @ E )
| ~ ( sum @ D @ F @ B )
| ~ ( sum @ E @ F @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_1) ).
thf(58,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ A @ D @ E )
| ~ ( sum @ D @ F @ B )
| ~ ( sum @ E @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(230,plain,
$false,
inference(cvc4,[status(thm)],[69,56,37,52,38,65,73,44,91,87,40,36,79,62,83,46,93,57,89,74,60,85,77,96,71,54,81,39,48,63,95,50,67,75,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD012-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n018.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 23:01:28 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.82/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/0.98 % [INFO] Parsing done (145ms).
% 1.13/0.99 % [INFO] Running in sequential loop mode.
% 1.72/1.21 % [INFO] eprover registered as external prover.
% 1.72/1.21 % [INFO] cvc4 registered as external prover.
% 1.72/1.22 % [INFO] Scanning for conjecture ...
% 1.83/1.28 % [INFO] Found a conjecture and 30 axioms. Running axiom selection ...
% 1.83/1.32 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.04/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.04/1.36 % [INFO] Type checking passed.
% 2.04/1.36 % [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 ...
% 5.37/2.22 % External prover 'cvc4' found a proof!
% 5.37/2.22 % [INFO] Killing All external provers ...
% 5.37/2.22 % Time passed: 1745ms (effective reasoning time: 1232ms)
% 5.37/2.22 % 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)>
% 5.37/2.22 % Axioms used in derivation (30): associativity_addition_1, existence_of_identity_multiplication, transitivity_of_order_relation, totality_of_multiplication, well_definedness_of_additive_identity, compatibility_of_order_relation_and_multiplication, a_is_defined, well_definedness_of_multiplication, existence_of_identity_addition, associativity_multiplication_1, antisymmetry_of_order_relation, totality_of_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_order_relation_and_addition, b_is_defined, totality_of_order_relation, existence_of_inverse_multiplication, well_definedness_of_multiplicative_identity, well_definedness_of_additive_inverse, distributivity_1, associativity_addition_2, commutativity_addition, associativity_multiplication_2, different_identities, well_definedness_of_multiplicative_inverse, u_is_defined, v_is_defined, distributivity_2
% 5.37/2.22 % No. of inferences in proof: 71
% 5.37/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1745 ms resp. 1232 ms w/o parsing
% 5.37/2.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.37/2.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------