TSTP Solution File: REL025+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : REL025+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:48:29 EDT 2023
% Result : Theorem 4.12s 2.17s
% Output : Refutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 38 ( 27 unt; 8 typ; 0 def)
% Number of atoms : 33 ( 32 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 178 ( 2 ~; 0 |; 0 &; 173 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 ^; 53 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(composition_type,type,
composition: $i > $i > $i ).
thf(top_type,type,
top: $i ).
thf(zero_type,type,
zero: $i ).
thf(15,axiom,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
thf(57,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
thf(27,plain,
! [A: $i,B: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
thf(54,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( join @ A @ one )
= one )
=> ( ( converse @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( join @ A @ one )
= one )
=> ( ( converse @ A )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i] :
( ( ( join @ A @ one )
= one )
=> ( ( converse @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
thf(42,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
thf(24,plain,
! [A: $i,B: $i,C: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i] :
( ( composition @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
thf(36,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(200,plain,
$false,
inference(e,[status(thm)],[57,45,27,54,39,48,16,42,24,21,33,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : REL025+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 18 17:32:46 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.88/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/0.92 % [INFO] Parsing done (126ms).
% 1.23/0.93 % [INFO] Running in sequential loop mode.
% 1.68/1.22 % [INFO] eprover registered as external prover.
% 1.68/1.22 % [INFO] cvc4 registered as external prover.
% 1.68/1.23 % [INFO] Scanning for conjecture ...
% 1.71/1.30 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.88/1.32 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.88/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 1.88/1.35 % [INFO] Type checking passed.
% 1.88/1.36 % [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 ...
% 4.12/2.17 % External prover 'e' found a proof!
% 4.12/2.17 % [INFO] Killing All external provers ...
% 4.12/2.17 % Time passed: 1678ms (effective reasoning time: 1231ms)
% 4.12/2.17 % 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)>
% 4.12/2.17 % Axioms used in derivation (13): converse_cancellativity, composition_identity, converse_idempotence, composition_associativity, maddux3_a_kind_of_de_Morgan, maddux2_join_associativity, maddux1_join_commutativity, converse_multiplicativity, converse_additivity, def_top, def_zero, composition_distributivity, maddux4_definiton_of_meet
% 4.12/2.17 % No. of inferences in proof: 30
% 4.12/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1678 ms resp. 1231 ms w/o parsing
% 4.12/2.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.12/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------