TSTP Solution File: REL005-4 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : REL005-4 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 : Tue May 21 02:32:40 EDT 2024
% Result : Unsatisfiable 3.69s 1.95s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of formulae : 45 ( 33 unt; 10 typ; 0 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 376 ( 4 ~; 2 |; 0 &; 370 @)
% ( 0 <=>; 0 =>; 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 : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 68 ( 0 ^ 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(composition_type,type,
composition: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(top_type,type,
top: $i ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
thf(41,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
thf(45,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [B: $i,A: $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_3) ).
thf(27,plain,
! [B: $i,A: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) )
= ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_1_15) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) )
= ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( ( join @ ( converse @ ( meet @ sk1 @ sk2 ) ) @ ( meet @ ( converse @ sk1 ) @ ( converse @ sk2 ) ) )
!= ( meet @ ( converse @ sk1 ) @ ( converse @ sk2 ) ) )
| ( ( join @ ( meet @ ( converse @ sk1 ) @ ( converse @ sk2 ) ) @ ( converse @ ( meet @ sk1 @ sk2 ) ) )
!= ( converse @ ( meet @ sk1 @ sk2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
thf(18,plain,
( ( ( join @ ( converse @ ( meet @ sk1 @ sk2 ) ) @ ( meet @ ( converse @ sk1 ) @ ( converse @ sk2 ) ) )
!= ( meet @ ( converse @ sk1 ) @ ( converse @ sk2 ) ) )
| ( ( join @ ( meet @ ( converse @ sk1 ) @ ( converse @ sk2 ) ) @ ( converse @ ( meet @ sk1 @ sk2 ) ) )
!= ( converse @ ( meet @ sk1 @ sk2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
thf(31,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) )
= ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law_14) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) )
= ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) )
= ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_2_16) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) )
= ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( composition @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
thf(21,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL005-4 : TPTP v8.2.0. Released v4.0.0.
% 0.16/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n024.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
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 08:12:54 EDT 2024
% 0.22/0.37 % CPUTime :
% 1.06/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/1.06 % [INFO] Parsing done (123ms).
% 1.37/1.07 % [INFO] Running in sequential loop mode.
% 1.83/1.29 % [INFO] eprover registered as external prover.
% 1.83/1.30 % [INFO] cvc4 registered as external prover.
% 1.83/1.30 % [INFO] Scanning for conjecture ...
% 2.06/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.16/1.40 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.16/1.42 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/1.42 % [INFO] Type checking passed.
% 2.16/1.43 % [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 ...
% 3.69/1.95 % External prover 'e' found a proof!
% 3.69/1.95 % [INFO] Killing All external provers ...
% 3.69/1.95 % Time passed: 1403ms (effective reasoning time: 877ms)
% 3.69/1.95 % Axioms used in derivation (16): maddux3_a_kind_of_de_Morgan_3, converse_idempotence_8, def_top_12, converse_cancellativity_11, composition_associativity_5, maddux2_join_associativity_2, composition_distributivity_7, maddux1_join_commutativity_1, modular_law_1_15, composition_identity_6, maddux4_definiton_of_meet_4, converse_additivity_9, dedekind_law_14, modular_law_2_16, def_zero_13, converse_multiplicativity_10
% 3.69/1.95 % No. of inferences in proof: 35
% 3.69/1.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1403 ms resp. 877 ms w/o parsing
% 3.87/1.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.87/1.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------