TSTP Solution File: LAT028-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT028-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 11:26:42 EDT 2023
% Result : Unsatisfiable 2.62s 1.60s
% Output : Refutation 2.91s
% 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 : 110 ( 2 ~; 0 |; 0 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_type,type,
meet: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(meet2_type,type,
meet2: $i > $i > $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_2) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ B ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( meet2 @ A @ B )
= ( meet2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet2) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( meet2 @ A @ B )
= ( meet2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(17,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( meet2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet2) ).
thf(27,plain,
! [A: $i] :
( ( meet2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( meet @ a @ b )
!= ( meet2 @ a @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',name) ).
thf(12,plain,
( ( meet @ a @ b )
!= ( meet2 @ a @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet2 @ ( meet2 @ ( join @ A @ B ) @ ( join @ C @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_1_2) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( meet2 @ ( meet2 @ ( join @ A @ B ) @ ( join @ C @ B ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ ( join @ A @ B ) @ ( join @ C @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_1) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ ( join @ A @ B ) @ ( join @ C @ B ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(15,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ ( meet2 @ A @ B ) @ ( meet2 @ C @ B ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_2_2) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ ( meet2 @ A @ B ) @ ( meet2 @ C @ B ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,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 : LAT028-1 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n026.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 14:41:21 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (115ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.50/1.18 % [INFO] eprover registered as external prover.
% 1.50/1.18 % [INFO] cvc4 registered as external prover.
% 1.71/1.18 % [INFO] Scanning for conjecture ...
% 1.79/1.23 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.87/1.25 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.87/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.26 % [INFO] Type checking passed.
% 1.87/1.27 % [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 ...
% 2.62/1.59 % External prover 'e' found a proof!
% 2.62/1.59 % [INFO] Killing All external provers ...
% 2.62/1.59 % Time passed: 1076ms (effective reasoning time: 619ms)
% 2.62/1.59 % 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)>
% 2.62/1.60 % Axioms used in derivation (10): commutativity_of_join, wal_2, wal_2_2, idempotence_of_join, commutativity_of_meet, idempotence_of_meet2, idempotence_of_meet, wal_1, commutativity_of_meet2, wal_1_2
% 2.62/1.60 % No. of inferences in proof: 23
% 2.62/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1076 ms resp. 619 ms w/o parsing
% 2.91/1.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.91/1.67 % [INFO] Killing All external provers ...
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