TSTP Solution File: BOO011-2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : BOO011-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 : Mon May 20 18:57:02 EDT 2024
% Result : Unsatisfiable 2.70s 1.64s
% Output : Refutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 36 ( 31 unt; 5 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 140 ( 2 ~; 0 |; 0 &; 138 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 ^ 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(inverse_type,type,
inverse: $i > $i ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(multiplicative_identity_type,type,
multiplicative_identity: $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ C ) )
= ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
thf(29,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)],[7]) ).
thf(13,axiom,
! [A: $i] :
( ( multiply @ multiplicative_identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id2) ).
thf(41,plain,
! [A: $i] :
( ( multiply @ multiplicative_identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i] :
( ( add @ additive_identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id2) ).
thf(45,plain,
! [A: $i] :
( ( add @ additive_identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ C )
= ( add @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ C )
= ( add @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i] :
( ( multiply @ A @ multiplicative_identity )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
thf(39,plain,
! [A: $i] :
( ( multiply @ A @ multiplicative_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(35,plain,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
thf(43,plain,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ ( multiply @ A @ B ) @ C )
= ( multiply @ ( add @ A @ C ) @ ( add @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ ( multiply @ A @ B ) @ C )
= ( multiply @ ( add @ A @ C ) @ ( add @ B @ 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/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
thf(37,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( multiply @ B @ C ) )
= ( multiply @ ( add @ A @ B ) @ ( add @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(25,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)],[5]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i] :
( ( add @ ( inverse @ A ) @ A )
= multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
thf(33,plain,
! [A: $i] :
( ( add @ ( inverse @ A ) @ A )
= multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( inverse @ additive_identity )
!= multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_1_is_0) ).
thf(16,plain,
( ( inverse @ additive_identity )
!= multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
thf(31,plain,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(47,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,39,35,43,23,19,37,25,21,33,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : BOO011-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n015.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 : Sat May 18 14:35:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.94/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/0.99 % [INFO] Parsing done (104ms).
% 1.36/0.99 % [INFO] Running in sequential loop mode.
% 1.64/1.21 % [INFO] eprover registered as external prover.
% 1.64/1.21 % [INFO] cvc4 registered as external prover.
% 1.64/1.22 % [INFO] Scanning for conjecture ...
% 1.85/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 1.95/1.29 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.95/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.95/1.31 % [INFO] Type checking passed.
% 1.95/1.31 % [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 ...
% 2.70/1.63 % External prover 'e' found a proof!
% 2.70/1.64 % [INFO] Killing All external provers ...
% 2.70/1.64 % Time passed: 1098ms (effective reasoning time: 639ms)
% 2.70/1.64 % Axioms used in derivation (14): distributivity3, distributivity2, multiplicative_inverse2, multiplicative_id2, multiplicative_inverse1, commutativity_of_add, multiplicative_id1, additive_inverse2, additive_inverse1, distributivity1, commutativity_of_multiply, additive_id2, distributivity4, additive_id1
% 2.70/1.64 % No. of inferences in proof: 31
% 2.70/1.64 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1098 ms resp. 639 ms w/o parsing
% 2.95/1.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.95/1.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------