TSTP Solution File: LAT010-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT010-1 : TPTP v8.1.2. Released v2.2.0.
% 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 11:26:39 EDT 2023
% Result : Unsatisfiable 18.07s 4.08s
% Output : Refutation 18.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 31 ( 25 unt; 6 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 278 ( 2 ~; 0 |; 0 &; 276 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% 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(d_type,type,
d: $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(24,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(20,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(28,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(1,negated_conjecture,
( ( meet @ a @ ( meet @ ( join @ b @ c ) @ ( join @ b @ d ) ) )
!= ( meet @ ( meet @ a @ ( meet @ ( join @ b @ c ) @ ( join @ b @ d ) ) ) @ ( join @ ( meet @ a @ ( join @ b @ ( meet @ c @ d ) ) ) @ ( join @ ( meet @ a @ c ) @ ( meet @ a @ d ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(13,plain,
( ( meet @ a @ ( meet @ ( join @ b @ c ) @ ( join @ b @ d ) ) )
!= ( meet @ ( meet @ a @ ( meet @ ( join @ b @ c ) @ ( join @ b @ d ) ) ) @ ( join @ ( meet @ a @ ( join @ b @ ( meet @ c @ d ) ) ) @ ( join @ ( meet @ a @ c ) @ ( meet @ a @ d ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(18,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(16,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(26,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ A @ D ) ) ) )
= ( join @ ( meet @ A @ ( join @ B @ ( meet @ A @ C ) ) ) @ ( meet @ A @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n5_1) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ A @ D ) ) ) )
= ( join @ ( meet @ A @ ( join @ B @ ( meet @ A @ C ) ) ) @ ( meet @ A @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ ( join @ C @ ( meet @ A @ D ) ) ) )
= ( meet @ ( join @ A @ ( meet @ B @ ( join @ A @ C ) ) ) @ ( join @ A @ ( meet @ ( join @ A @ B ) @ ( join @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n5_2) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ ( join @ C @ ( meet @ A @ D ) ) ) )
= ( meet @ ( join @ A @ ( meet @ B @ ( join @ A @ C ) ) ) @ ( join @ A @ ( meet @ ( join @ A @ B ) @ ( join @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( join @ A @ ( meet @ B @ C ) ) @ ( join @ C @ ( meet @ A @ B ) ) )
= ( join @ ( meet @ C @ ( join @ A @ ( meet @ B @ C ) ) ) @ ( meet @ A @ ( join @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nr_3) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( join @ A @ ( meet @ B @ C ) ) @ ( join @ C @ ( meet @ A @ B ) ) )
= ( join @ ( meet @ C @ ( join @ A @ ( meet @ B @ C ) ) ) @ ( meet @ A @ ( join @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(30,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(3751,plain,
$false,
inference(e,[status(thm)],[24,20,28,13,22,18,16,26,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT010-1 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n022.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Thu May 18 14:25:03 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.89/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.00 % [INFO] Parsing done (120ms).
% 1.36/1.01 % [INFO] Running in sequential loop mode.
% 1.69/1.21 % [INFO] eprover registered as external prover.
% 1.69/1.21 % [INFO] cvc4 registered as external prover.
% 1.69/1.22 % [INFO] Scanning for conjecture ...
% 1.92/1.28 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.98/1.32 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.01/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.01/1.35 % [INFO] Type checking passed.
% 2.01/1.36 % [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 ...
% 18.07/4.07 % External prover 'e' found a proof!
% 18.07/4.07 % [INFO] Killing All external provers ...
% 18.07/4.08 % Time passed: 3536ms (effective reasoning time: 3062ms)
% 18.07/4.08 % 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)>
% 18.07/4.08 % Axioms used in derivation (11): nr_3, commutativity_of_join, absorption1, associativity_of_meet, commutativity_of_meet, n5_2, associativity_of_join, idempotence_of_meet, n5_1, idempotence_of_join, absorption2
% 18.07/4.08 % No. of inferences in proof: 25
% 18.07/4.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3536 ms resp. 3062 ms w/o parsing
% 18.07/4.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.07/4.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------