TSTP Solution File: BOO029-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : BOO029-1 : TPTP v8.1.2. Released v2.2.0.
% 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 10:11:59 EDT 2023
% Result : Unsatisfiable 2.63s 1.61s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 28 ( 23 unt; 5 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 146 ( 2 ~; 0 |; 0 &; 144 @)
% ( 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 : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(add_type,type,
add: $i > $i > $i ).
thf(b_type,type,
b: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(a_type,type,
a: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ ( inverse @ B ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ ( inverse @ B ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B )
= ( multiply @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ ( add @ ( multiply @ A @ B ) @ ( multiply @ B @ C ) ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ ( add @ ( multiply @ A @ B ) @ ( multiply @ B @ C ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( add @ A @ B )
= ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( add @ b @ ( inverse @ b ) )
!= ( add @ a @ ( inverse @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_inverse) ).
thf(12,plain,
( ( add @ b @ ( inverse @ b ) )
!= ( add @ a @ ( inverse @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ ( add @ A @ B ) @ C )
= ( add @ A @ ( add @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ ( add @ A @ B ) @ C )
= ( add @ A @ ( add @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ ( add @ A @ B ) @ ( add @ B @ C ) ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ ( add @ A @ B ) @ ( add @ B @ C ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ ( add @ A @ ( inverse @ B ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ ( add @ A @ ( inverse @ B ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( multiply @ B @ ( multiply @ A @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( multiply @ B @ ( multiply @ A @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ ( add @ A @ C ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ ( add @ A @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiply) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[25,29,17,27,12,31,23,19,15,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO029-1 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 21:05:43 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (112ms).
% 1.22/0.95 % [INFO] Running in sequential loop mode.
% 1.61/1.15 % [INFO] eprover registered as external prover.
% 1.61/1.15 % [INFO] cvc4 registered as external prover.
% 1.61/1.16 % [INFO] Scanning for conjecture ...
% 1.70/1.21 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.70/1.22 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.86/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.86/1.24 % [INFO] Type checking passed.
% 1.86/1.24 % [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 ...
% 2.63/1.60 % External prover 'e' found a proof!
% 2.63/1.60 % [INFO] Killing All external provers ...
% 2.63/1.60 % Time passed: 1088ms (effective reasoning time: 646ms)
% 2.63/1.60 % 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)>
% 2.63/1.61 % Axioms used in derivation (10): b2, b1, commutativity_of_multiply, l2, l4, l3, l1, associativity_of_add, commutativity_of_add, associativity_of_multiply
% 2.63/1.61 % No. of inferences in proof: 23
% 2.63/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1088 ms resp. 646 ms w/o parsing
% 3.02/1.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.02/1.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------