TSTP Solution File: BOO012-4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : BOO012-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 10:11:54 EDT 2023
% Result : Unsatisfiable 2.67s 1.57s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 25 ( 19 unt; 6 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 82 ( 2 ~; 0 |; 0 &; 80 @)
% ( 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 : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(inverse_type,type,
inverse: $i > $i ).
thf(x_type,type,
x: $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(1,negated_conjecture,
( ( inverse @ ( inverse @ x ) )
!= x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
thf(10,plain,
( ( inverse @ ( inverse @ x ) )
!= x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
thf(25,plain,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).
thf(21,plain,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(17,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(9,axiom,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(27,plain,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i] :
( ( multiply @ A @ multiplicative_identity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).
thf(23,plain,
! [A: $i] :
( ( multiply @ A @ multiplicative_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(19,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(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,plain,
$false,
inference(e,[status(thm)],[10,25,21,13,17,27,23,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO012-4 : TPTP v8.1.2. Released v1.1.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 21:02:33 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.95 % [INFO] Parsing done (106ms).
% 1.16/0.96 % [INFO] Running in sequential loop mode.
% 1.63/1.15 % [INFO] eprover registered as external prover.
% 1.63/1.15 % [INFO] cvc4 registered as external prover.
% 1.63/1.16 % [INFO] Scanning for conjecture ...
% 1.71/1.20 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.71/1.22 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.84/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.23 % [INFO] Type checking passed.
% 1.84/1.23 % [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 ...
% 2.67/1.56 % External prover 'e' found a proof!
% 2.67/1.56 % [INFO] Killing All external provers ...
% 2.67/1.57 % Time passed: 1044ms (effective reasoning time: 605ms)
% 2.67/1.57 % 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)>
% 2.67/1.57 % Axioms used in derivation (8): distributivity2, commutativity_of_multiply, multiplicative_inverse1, additive_id1, commutativity_of_add, multiplicative_id1, additive_inverse1, distributivity1
% 2.67/1.57 % No. of inferences in proof: 19
% 2.67/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1044 ms resp. 605 ms w/o parsing
% 2.67/1.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.67/1.64 % [INFO] Killing All external provers ...
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