TSTP Solution File: LAT005-3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT005-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:26:38 EDT 2023
% Result : Unsatisfiable 3.97s 1.90s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 28
% Syntax : Number of formulae : 48 ( 31 unt; 9 typ; 0 def)
% Number of atoms : 49 ( 38 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 194 ( 12 ~; 10 |; 0 &; 172 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_type,type,
r1: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(r2_type,type,
r2: $i ).
thf(b_type,type,
b: $i ).
thf(a_type,type,
a: $i ).
thf(n1_type,type,
n1: $i ).
thf(n0_type,type,
n0: $i ).
thf(complement_type,type,
complement: $i > $i > $o ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ A @ B )
!= A )
| ( ( meet @ B @ ( join @ A @ C ) )
= ( join @ A @ ( meet @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ A @ B )
!= A )
| ( ( meet @ B @ ( join @ A @ C ) )
= ( join @ A @ ( meet @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(53,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
thf(41,plain,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
complement @ r2 @ ( meet @ a @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
thf(35,plain,
complement @ r2 @ ( meet @ a @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( ( meet @ A @ B )
!= n0 )
| ( ( join @ A @ B )
!= n1 )
| ( complement @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( meet @ A @ B )
!= n0 )
| ( ( join @ A @ B )
!= n1 )
| ( complement @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( complement @ A @ B )
| ( ( join @ A @ B )
= n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( complement @ A @ B )
| ( ( join @ A @ B )
= n1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
( r1
!= ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).
thf(20,plain,
( r1
!= ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).
thf(29,plain,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( complement @ A @ B )
| ( ( meet @ A @ B )
= n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( complement @ A @ B )
| ( ( meet @ A @ B )
= n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
thf(33,plain,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
thf(27,plain,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
complement @ r1 @ ( join @ a @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).
thf(55,plain,
complement @ r1 @ ( join @ a @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(23,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(36,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)],[9]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
thf(51,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)],[15]) ).
thf(179,plain,
$false,
inference(e,[status(thm)],[56,25,53,41,35,48,31,43,20,46,29,38,33,59,27,55,23,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT005-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu May 18 14:34:35 EDT 2023
% 0.18/0.32 % CPUTime :
% 0.73/0.75 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.08/0.88 % [INFO] Parsing done (133ms).
% 1.17/0.89 % [INFO] Running in sequential loop mode.
% 1.55/1.09 % [INFO] eprover registered as external prover.
% 1.55/1.10 % [INFO] cvc4 registered as external prover.
% 1.55/1.10 % [INFO] Scanning for conjecture ...
% 1.55/1.15 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.55/1.18 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.82/1.20 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.21 % [INFO] Type checking passed.
% 1.87/1.21 % [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 ...
% 3.97/1.89 % External prover 'e' found a proof!
% 3.97/1.90 % [INFO] Killing All external provers ...
% 3.97/1.90 % Time passed: 1467ms (effective reasoning time: 1000ms)
% 3.97/1.90 % 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)>
% 3.97/1.90 % Axioms used in derivation (18): commutativity_of_join, meet_join_complement, commutativity_of_meet, x_join_0, x_meet_1, associativity_of_join, idempotence_of_meet, x_meet_0, complement_of_a_meet_b, absorption1, x_join_1, modular, associativity_of_meet, complement_join, complement_meet, complement_of_a_join_b, idempotence_of_join, absorption2
% 3.97/1.90 % No. of inferences in proof: 39
% 3.97/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1467 ms resp. 1000 ms w/o parsing
% 4.02/1.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.02/1.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------