TSTP Solution File: LAT241-10 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT241-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 11:27:05 EDT 2023
% Result : Unsatisfiable 3.89s 1.85s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 39 ( 31 unt; 8 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 170 ( 2 ~; 0 |; 0 &; 168 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(b_type,type,
b: $i ).
thf(a_type,type,
a: $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(zero_type,type,
zero: $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
thf(41,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(15,axiom,
( ( meet @ b @ a )
= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
thf(45,plain,
( ( meet @ b @ a )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
thf(39,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,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(35,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(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ A @ D ) ) ) )
= ( meet @ A @ ( join @ B @ ( join @ ( meet @ A @ C ) @ ( meet @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H51) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ ( meet @ C @ ( join @ A @ D ) ) ) )
= ( meet @ A @ ( join @ B @ ( join @ ( meet @ A @ C ) @ ( meet @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
thf(37,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(21,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,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(33,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(1,negated_conjecture,
( ( join @ ( complement @ b ) @ ( complement @ a ) )
!= ( complement @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
thf(16,plain,
( ( join @ ( complement @ b ) @ ( complement @ a ) )
!= ( complement @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox2/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)],[8]) ).
thf(79,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,39,35,43,23,19,37,25,21,33,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT241-10 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.34 % Computer : n010.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu May 18 13:54:28 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.91/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (150ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.52/1.17 % [INFO] eprover registered as external prover.
% 1.52/1.17 % [INFO] cvc4 registered as external prover.
% 1.72/1.18 % [INFO] Scanning for conjecture ...
% 1.84/1.24 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.84/1.26 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.84/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.28 % [INFO] Type checking passed.
% 1.84/1.28 % [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 ...
% 3.89/1.84 % External prover 'e' found a proof!
% 3.89/1.84 % [INFO] Killing All external provers ...
% 3.89/1.85 % Time passed: 1350ms (effective reasoning time: 869ms)
% 3.89/1.85 % 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)>
% 3.89/1.85 % Axioms used in derivation (14): equation_H51, absorption1, meet_join_complement, complement_meet, commutativity_of_meet, associativity_of_join, idempotence_of_meet, prove_distributivity_hypothesis, ifeq_axiom, commutativity_of_join, associativity_of_meet, complement_join, idempotence_of_join, absorption2
% 3.89/1.85 % No. of inferences in proof: 31
% 3.89/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1350 ms resp. 869 ms w/o parsing
% 3.89/1.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.89/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------