TSTP Solution File: LAT036-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT036-1 : TPTP v8.1.2. Released v2.4.0.
% 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 11:26:43 EDT 2023
% Result : Unsatisfiable 3.97s 2.01s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 57 ( 47 unt; 8 typ; 0 def)
% Number of atoms : 51 ( 50 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 348 ( 4 ~; 2 |; 0 &; 342 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(k_type,type,
k: $i > $i ).
thf(aa_type,type,
aa: $i ).
thf(bb_type,type,
bb: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(cc_type,type,
cc: $i ).
thf(n1_type,type,
n1: $i ).
thf(n0_type,type,
n0: $i ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ C ) )
= ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_meet) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ C ) )
= ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
thf(56,plain,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
( ( k @ n1 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_top) ).
thf(52,plain,
( ( k @ n1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
( ( join @ ( k @ ( k @ ( k @ bb ) ) ) @ ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) )
= ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs4) ).
thf(46,plain,
( ( join @ ( k @ ( k @ ( k @ bb ) ) ) @ ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) )
= ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,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(60,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)],[18]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( k @ ( join @ A @ B ) )
= ( meet @ ( k @ A ) @ ( k @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_join) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( k @ ( join @ A @ B ) )
= ( meet @ ( k @ A ) @ ( k @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(44,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
( ( k @ n0 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_bottom) ).
thf(48,plain,
( ( k @ n0 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( k @ ( meet @ A @ B ) )
= ( join @ ( k @ A ) @ ( k @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_meet) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( k @ ( meet @ A @ B ) )
= ( join @ ( k @ A ) @ ( k @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
( ( join @ ( k @ ( k @ aa ) ) @ ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) )
= ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs3) ).
thf(58,plain,
( ( join @ ( k @ ( k @ aa ) ) @ ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) )
= ( join @ ( k @ aa ) @ ( join @ ( k @ bb ) @ ( k @ cc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,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(62,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)],[19]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ C ) )
= ( meet @ ( join @ A @ B ) @ ( join @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_join) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ C ) )
= ( meet @ ( join @ A @ B ) @ ( join @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( join @ ( k @ ( k @ ( join @ aa @ ( k @ bb ) ) ) ) @ ( join @ ( meet @ aa @ ( k @ ( meet @ bb @ cc ) ) ) @ ( k @ aa ) ) )
!= ( join @ ( meet @ aa @ ( k @ ( meet @ bb @ cc ) ) ) @ ( k @ aa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
thf(25,plain,
( ( join @ ( k @ ( k @ ( join @ aa @ ( k @ bb ) ) ) ) @ ( join @ ( meet @ aa @ ( k @ ( meet @ bb @ cc ) ) ) @ ( k @ aa ) ) )
!= ( join @ ( meet @ aa @ ( k @ ( meet @ bb @ cc ) ) ) @ ( k @ aa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(28,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
thf(32,plain,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).
thf(34,plain,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,axiom,
( ( join @ ( k @ ( k @ ( k @ bb ) ) ) @ ( join @ aa @ ( k @ aa ) ) )
= ( join @ aa @ ( k @ aa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
thf(71,plain,
( ( join @ ( k @ ( k @ ( k @ bb ) ) ) @ ( join @ aa @ ( k @ aa ) ) )
= ( join @ aa @ ( k @ aa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
( ( join @ ( k @ ( k @ aa ) ) @ ( join @ aa @ ( k @ aa ) ) )
= ( join @ aa @ ( k @ aa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
thf(54,plain,
( ( join @ ( k @ ( k @ aa ) ) @ ( join @ aa @ ( k @ aa ) ) )
= ( join @ aa @ ( k @ aa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,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(50,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)],[13]) ).
thf(21,axiom,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
thf(67,plain,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(147,plain,
$false,
inference(e,[status(thm)],[69,56,52,46,60,65,73,44,48,40,58,62,42,25,28,38,32,34,71,54,50,67,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LAT036-1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n021.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 14:26:58 EDT 2023
% 0.17/0.38 % CPUTime :
% 1.00/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.01 % [INFO] Parsing done (130ms).
% 1.20/1.02 % [INFO] Running in sequential loop mode.
% 1.74/1.22 % [INFO] eprover registered as external prover.
% 1.74/1.23 % [INFO] cvc4 registered as external prover.
% 1.74/1.23 % [INFO] Scanning for conjecture ...
% 1.88/1.29 % [INFO] Found a conjecture and 23 axioms. Running axiom selection ...
% 2.03/1.33 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.03/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.03/1.36 % [INFO] Type checking passed.
% 2.24/1.36 % [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 ...
% 3.97/2.00 % External prover 'e' found a proof!
% 3.97/2.00 % [INFO] Killing All external provers ...
% 3.97/2.00 % Time passed: 1454ms (effective reasoning time: 978ms)
% 3.97/2.00 % 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)>
% 3.97/2.01 % Axioms used in derivation (23): commutativity_of_join, lhs1, k_on_join, k_on_top, commutativity_of_meet, k_on_meet, x_meet_1, associativity_of_join, idempotence_of_meet, lhs3, dist_join, absorption1, x_join_1, modular, associativity_of_meet, lhs4, idempotence_of_join, absorption2, k_on_bottom, lhs2, x_join_0, x_meet_0, dist_meet
% 3.97/2.01 % No. of inferences in proof: 49
% 3.97/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1454 ms resp. 978 ms w/o parsing
% 3.97/2.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.97/2.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------