TSTP Solution File: SEU244+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU244+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 11:57:48 EDT 2023
% Result : Theorem 3.20s 1.79s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 32
% Syntax : Number of formulae : 49 ( 13 unt; 17 typ; 0 def)
% Number of atoms : 108 ( 6 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 249 ( 2 ~; 0 |; 32 &; 171 @)
% ( 9 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(well_orders_type,type,
well_orders: $i > $i > $o ).
thf(relation_field_type,type,
relation_field: $i > $i ).
thf(well_ordering_type,type,
well_ordering: $i > $o ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(antisymmetric_type,type,
antisymmetric: $i > $o ).
thf(is_antisymmetric_in_type,type,
is_antisymmetric_in: $i > $i > $o ).
thf(connected_type,type,
connected: $i > $o ).
thf(is_connected_in_type,type,
is_connected_in: $i > $i > $o ).
thf(transitive_type,type,
transitive: $i > $o ).
thf(is_transitive_in_type,type,
is_transitive_in: $i > $i > $o ).
thf(reflexive_type,type,
reflexive: $i > $o ).
thf(well_founded_relation_type,type,
well_founded_relation: $i > $o ).
thf(is_reflexive_in_type,type,
is_reflexive_in: $i > $i > $o ).
thf(is_well_founded_in_type,type,
is_well_founded_in: $i > $i > $o ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(relation_rng_type,type,
relation_rng: $i > $i ).
thf(8,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( well_orders @ A @ B )
<=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
thf(42,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( well_orders @ A @ B )
=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) )
& ( ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) )
=> ( well_orders @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(61,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(60,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(59,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
thf(54,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( reflexive @ A )
=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) )
& ( ( is_reflexive_in @ A @ ( relation_field @ A ) )
=> ( reflexive @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
thf(35,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( well_ordering @ A )
=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) )
& ( ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) )
=> ( well_ordering @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(58,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(51,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(57,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
thf(29,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( connected @ A )
=> ( is_connected_in @ A @ ( relation_field @ A ) ) )
& ( ( is_connected_in @ A @ ( relation_field @ A ) )
=> ( connected @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
thf(32,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( transitive @ A )
=> ( is_transitive_in @ A @ ( relation_field @ A ) ) )
& ( ( is_transitive_in @ A @ ( relation_field @ A ) )
=> ( transitive @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
thf(64,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( well_founded_relation @ A )
=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) )
& ( ( is_well_founded_in @ A @ ( relation_field @ A ) )
=> ( well_founded_relation @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i] :
( ( relation @ A )
=> ( ( ( well_orders @ A @ ( relation_field @ A ) )
=> ( well_ordering @ A ) )
& ( ( well_ordering @ A )
=> ( well_orders @ A @ ( relation_field @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
thf(26,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( antisymmetric @ A )
=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) )
& ( ( is_antisymmetric_in @ A @ ( relation_field @ A ) )
=> ( antisymmetric @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(67,plain,
$false,
inference(cvc4,[status(thm)],[42,61,60,59,54,35,58,51,57,29,32,64,17,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU244+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 18 13:39:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.81/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.08/0.99 % [INFO] Parsing done (125ms).
% 1.08/1.00 % [INFO] Running in sequential loop mode.
% 1.61/1.22 % [INFO] eprover registered as external prover.
% 1.61/1.22 % [INFO] cvc4 registered as external prover.
% 1.61/1.23 % [INFO] Scanning for conjecture ...
% 1.69/1.29 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.69/1.31 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.99/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 1.99/1.33 % [INFO] Type checking passed.
% 1.99/1.34 % [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 ...
% 2.94/1.79 % External prover 'cvc4' found a proof!
% 2.94/1.79 % [INFO] Killing All external provers ...
% 2.94/1.79 % Time passed: 1285ms (effective reasoning time: 787ms)
% 2.94/1.79 % 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)>
% 2.94/1.79 % Axioms used in derivation (14): dt_k3_relat_1, dt_k2_relat_1, d4_wellord1, d14_relat_2, d6_relat_1, idempotence_k2_xboole_0, d9_relat_2, commutativity_k2_xboole_0, d12_relat_2, dt_k2_xboole_0, d5_wellord1, t5_wellord1, d16_relat_2, dt_k1_relat_1
% 2.94/1.79 % No. of inferences in proof: 32
% 3.20/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1285 ms resp. 787 ms w/o parsing
% 3.32/1.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.32/1.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------