TSTP Solution File: LAT186-10 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT186-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:26:57 EDT 2023
% Result : Unsatisfiable 9.53s 2.93s
% Output : Refutation 9.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 38 ( 29 unt; 9 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 180 ( 2 ~; 0 |; 0 &; 178 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% 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(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(one_type,type,
one: $i ).
thf(zero_type,type,
zero: $i ).
thf(3,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(20,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(22,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( meet @ a @ ( join @ b @ c ) )
!= ( join @ ( meet @ a @ b ) @ ( meet @ a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
thf(15,plain,
( ( meet @ a @ ( join @ b @ c ) )
!= ( join @ ( meet @ a @ b ) @ ( meet @ a @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ A @ C ) ) )
= ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ A @ ( meet @ B @ ( join @ C @ ( meet @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H11) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ A @ C ) ) )
= ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ A @ ( meet @ B @ ( join @ C @ ( meet @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
thf(38,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(32,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(10,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(34,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)],[10]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( join @ A @ B ) @ one @ ( ifeq @ ( meet @ A @ B ) @ zero @ ( complement @ A ) @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( join @ A @ B ) @ one @ ( ifeq @ ( meet @ A @ B ) @ zero @ ( complement @ A ) @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).
thf(36,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(895,plain,
$false,
inference(e,[status(thm)],[20,22,18,15,42,24,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT186-10 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n001.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 14:36:20 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.02 % [INFO] Parsing done (126ms).
% 1.28/1.03 % [INFO] Running in sequential loop mode.
% 1.69/1.24 % [INFO] eprover registered as external prover.
% 1.69/1.24 % [INFO] cvc4 registered as external prover.
% 1.78/1.24 % [INFO] Scanning for conjecture ...
% 1.78/1.30 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.78/1.32 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.00/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 2.00/1.34 % [INFO] Type checking passed.
% 2.00/1.34 % [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 ...
% 9.53/2.93 % External prover 'e' found a proof!
% 9.53/2.93 % [INFO] Killing All external provers ...
% 9.53/2.93 % Time passed: 2400ms (effective reasoning time: 1897ms)
% 9.53/2.93 % 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)>
% 9.53/2.93 % Axioms used in derivation (13): meet_join_complement, complement_meet, commutativity_of_meet, associativity_of_join, idempotence_of_meet, ifeq_axiom, commutativity_of_join, absorption1, equation_H11, associativity_of_meet, complement_join, idempotence_of_join, absorption2
% 9.53/2.93 % No. of inferences in proof: 29
% 9.53/2.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2400 ms resp. 1897 ms w/o parsing
% 9.53/2.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.53/2.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------