TSTP Solution File: BOO013-4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : BOO013-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 10:11:55 EDT 2023
% Result : Unsatisfiable 2.71s 1.67s
% Output : Refutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 30 ( 23 unt; 7 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 88 ( 2 ~; 0 |; 0 &; 86 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(a_type,type,
a: $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(multiplicative_identity_type,type,
multiplicative_identity: $i ).
thf(7,axiom,
! [A: $i] :
( ( multiply @ A @ multiplicative_identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).
thf(25,plain,
! [A: $i] :
( ( multiply @ A @ multiplicative_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(29,plain,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
thf(27,plain,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( b
!= ( inverse @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_is_b) ).
thf(12,plain,
( b
!= ( inverse @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
( ( add @ a @ b )
= multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_a_multiplicative_identity) ).
thf(31,plain,
( ( add @ a @ b )
= multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).
thf(23,plain,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( multiply @ B @ C ) )
= ( multiply @ ( add @ A @ B ) @ ( add @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( multiply @ B @ C ) )
= ( multiply @ ( add @ A @ B ) @ ( add @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ C ) )
= ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ C ) )
= ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
( ( multiply @ a @ b )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_an_additive_identity) ).
thf(33,plain,
( ( multiply @ a @ b )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[25,29,17,27,12,31,23,19,15,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : BOO013-4 : TPTP v8.1.2. Released v1.1.0.
% 0.08/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n021.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 21:02:28 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.04 % [INFO] Parsing done (127ms).
% 1.31/1.04 % [INFO] Running in sequential loop mode.
% 1.74/1.25 % [INFO] eprover registered as external prover.
% 1.74/1.25 % [INFO] cvc4 registered as external prover.
% 1.74/1.25 % [INFO] Scanning for conjecture ...
% 1.74/1.30 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.94/1.31 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.94/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.33 % [INFO] Type checking passed.
% 1.94/1.33 % [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 ...
% 2.71/1.67 % External prover 'e' found a proof!
% 2.71/1.67 % [INFO] Killing All external provers ...
% 2.71/1.67 % Time passed: 1140ms (effective reasoning time: 624ms)
% 2.71/1.67 % 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)>
% 2.71/1.67 % Axioms used in derivation (10): b_an_additive_identity, distributivity2, commutativity_of_multiply, multiplicative_inverse1, additive_id1, b_a_multiplicative_identity, commutativity_of_add, multiplicative_id1, additive_inverse1, distributivity1
% 2.71/1.67 % No. of inferences in proof: 23
% 2.71/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1140 ms resp. 624 ms w/o parsing
% 2.97/1.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.97/1.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------