TSTP Solution File: LAT066-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT066-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:26:46 EDT 2023
% Result : Unsatisfiable 3.85s 1.84s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 35 ( 25 unt; 8 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 164 ( 6 ~; 4 |; 0 &; 154 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_type,type,
meet: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(n1_type,type,
n1: $i ).
thf(n0_type,type,
n0: $i ).
thf(1,negated_conjecture,
( ( meet @ a @ ( join @ b @ c ) )
!= ( join @ ( meet @ a @ b ) @ ( meet @ a @ c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
thf(14,plain,
( ( meet @ a @ ( join @ b @ c ) )
!= ( join @ ( meet @ a @ b ) @ ( meet @ a @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(17,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom) ).
thf(35,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(19,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ( join @ A @ B )
!= n1 )
| ( ( meet @ A @ B )
!= n0 )
| ( ( complement @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complements_are_unique) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( join @ A @ B )
!= n1 )
| ( ( meet @ A @ B )
!= n0 )
| ( ( complement @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',top) ).
thf(33,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( join @ C @ ( meet @ D @ ( join @ A @ ( meet @ B @ C ) ) ) ) ) )
= ( meet @ A @ ( join @ B @ ( join @ C @ ( meet @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g61) ).
thf(40,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( join @ C @ ( meet @ D @ ( join @ A @ ( meet @ B @ C ) ) ) ) ) )
= ( meet @ A @ ( join @ B @ ( join @ C @ ( meet @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(84,plain,
$false,
inference(e,[status(thm)],[14,29,17,27,35,31,19,37,25,21,33,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LAT066-1 : TPTP v8.1.2. Released v2.5.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n009.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 : Thu May 18 14:11:19 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.10/1.01 % [INFO] Parsing done (124ms).
% 1.10/1.02 % [INFO] Running in sequential loop mode.
% 1.70/1.21 % [INFO] eprover registered as external prover.
% 1.70/1.21 % [INFO] cvc4 registered as external prover.
% 1.70/1.22 % [INFO] Scanning for conjecture ...
% 1.84/1.27 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.84/1.29 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.84/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.31 % [INFO] Type checking passed.
% 2.02/1.31 % [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 ...
% 3.85/1.83 % External prover 'e' found a proof!
% 3.85/1.83 % [INFO] Killing All external provers ...
% 3.85/1.83 % Time passed: 1287ms (effective reasoning time: 813ms)
% 3.85/1.83 % 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)>
% 3.85/1.84 % Axioms used in derivation (12): commutativity_of_join, absorption1, commutativity_of_meet, complements_are_unique, g61, associativity_of_join, idempotence_of_meet, top, associativity_of_meet, bottom, idempotence_of_join, absorption2
% 3.85/1.84 % No. of inferences in proof: 27
% 3.85/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1287 ms resp. 813 ms w/o parsing
% 3.85/1.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.85/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------