TSTP Solution File: FLD031-3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : FLD031-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:07:51 EDT 2023
% Result : Unsatisfiable 2.72s 1.58s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 41
% Syntax : Number of formulae : 72 ( 15 unt; 11 typ; 0 def)
% Number of atoms : 163 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 600 ( 102 ~; 102 |; 0 &; 396 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 146 ( 0 ^; 146 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(multiplicative_identity_type,type,
multiplicative_identity: $i ).
thf(a_type,type,
a: $i ).
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $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(22,axiom,
! [A: $i] :
( ( product @ multiplicative_identity @ A @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(69,plain,
! [A: $i] :
( ( product @ multiplicative_identity @ A @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( defined @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( defined @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
defined @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(61,plain,
defined @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,axiom,
! [A: $i] :
( ( sum @ additive_identity @ A @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(85,plain,
! [A: $i] :
( ( sum @ additive_identity @ A @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( sum @ A @ B @ C )
| ~ ( sum @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [A: $i] :
( ( sum @ ( additive_inverse @ A ) @ A @ additive_identity )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(53,plain,
! [A: $i] :
( ( sum @ ( additive_inverse @ A ) @ A @ additive_identity )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
thf(77,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)],[26]) ).
thf(24,axiom,
! [A: $i] :
( ( product @ ( multiplicative_inverse @ A ) @ A @ multiplicative_identity )
| ( sum @ additive_identity @ A @ additive_identity )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(73,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)],[24]) ).
thf(2,negated_conjecture,
~ ( sum @ additive_identity @ a @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
thf(32,plain,
~ ( sum @ additive_identity @ a @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
~ ( sum @ additive_identity @ additive_identity @ multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(81,plain,
~ ( sum @ additive_identity @ additive_identity @ multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( sum @ A @ B @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_addition) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( sum @ A @ B @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(18,axiom,
defined @ additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(62,plain,
defined @ additive_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(83,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)],[29]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
thf(46,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)],[9]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',distributivity_2) ).
thf(57,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)],[15]) ).
thf(5,axiom,
! [A: $i] :
( ( defined @ ( additive_inverse @ A ) )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(38,plain,
! [A: $i] :
( ( defined @ ( additive_inverse @ A ) )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,negated_conjecture,
~ ( product @ multiplicative_identity @ ( multiplicative_inverse @ a ) @ multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_4) ).
thf(33,plain,
~ ( product @ multiplicative_identity @ ( multiplicative_inverse @ a ) @ multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( defined @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( defined @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(59,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)],[16]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
thf(71,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)],[23]) ).
thf(11,axiom,
! [A: $i] :
( ( defined @ ( multiplicative_inverse @ A ) )
| ~ ( defined @ A )
| ( sum @ additive_identity @ A @ additive_identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(49,plain,
! [A: $i] :
( ( defined @ ( multiplicative_inverse @ A ) )
| ~ ( defined @ A )
| ( sum @ additive_identity @ A @ additive_identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
defined @ multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(48,plain,
defined @ multiplicative_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( sum @ additive_identity @ A @ B )
| ~ ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(63,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)],[19]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
thf(67,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)],[21]) ).
thf(1,negated_conjecture,
product @ multiplicative_identity @ a @ multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_2) ).
thf(31,plain,
product @ multiplicative_identity @ a @ multiplicative_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ( less_or_equal @ B @ A )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(40,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)],[6]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( product @ A @ B @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_multiplication) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( product @ A @ B @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(36,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)],[4]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
thf(51,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)],[12]) ).
thf(87,plain,
$false,
inference(e,[status(thm)],[69,42,61,85,65,53,77,73,32,81,75,79,62,83,46,57,38,33,44,59,71,49,48,63,67,31,40,55,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : FLD031-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.10 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Thu May 18 22:52:20 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.64/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.91/0.85 % [INFO] Parsing done (127ms).
% 0.91/0.86 % [INFO] Running in sequential loop mode.
% 1.45/1.06 % [INFO] eprover registered as external prover.
% 1.45/1.06 % [INFO] cvc4 registered as external prover.
% 1.45/1.06 % [INFO] Scanning for conjecture ...
% 1.63/1.11 % [INFO] Found a conjecture and 27 axioms. Running axiom selection ...
% 1.63/1.15 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 1.88/1.19 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/1.19 % [INFO] Type checking passed.
% 1.88/1.19 % [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 ...
% 2.72/1.58 % External prover 'e' found a proof!
% 2.72/1.58 % [INFO] Killing All external provers ...
% 2.72/1.58 % Time passed: 1172ms (effective reasoning time: 717ms)
% 2.72/1.58 % 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)>
% 2.72/1.58 % Axioms used in derivation (27): 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_order_relation, totality_of_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_order_relation_and_addition, distributivity_2, 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
% 2.72/1.58 % No. of inferences in proof: 61
% 2.72/1.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1172 ms resp. 717 ms w/o parsing
% 3.01/1.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.01/1.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------