TSTP Solution File: SEU254+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU254+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:57:51 EDT 2023
% Result : Theorem 3.40s 1.93s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 41
% Syntax : Number of formulae : 70 ( 21 unt; 14 typ; 0 def)
% Number of atoms : 132 ( 16 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 354 ( 14 ~; 2 |; 36 &; 264 @)
% ( 3 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 0 ^; 88 !; 12 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(transitive_type,type,
transitive: $i > $o ).
thf(relation_restriction_type,type,
relation_restriction: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(function_type,type,
function: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(26,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
thf(101,plain,
! [A: $i] :
( ( relation @ A )
=> ( ( ( transitive @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) )
& ( ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( transitive @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(56,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(42,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(53,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(28,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(109,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(81,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(72,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( in @ A @ C )
& ( in @ B @ D ) ) )
& ( ( ( in @ A @ C )
& ( in @ B @ D ) )
=> ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(36,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
thf(94,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(62,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(46,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(38,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(97,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(59,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(49,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_restriction @ C @ B ) )
<=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
thf(86,plain,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( ( in @ A @ ( relation_restriction @ C @ B ) )
=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) )
& ( ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) )
=> ( in @ A @ ( relation_restriction @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(50,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(90,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(83,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(113,plain,
$false,
inference(e,[status(thm)],[101,56,42,106,53,109,81,72,36,94,62,46,78,29,38,70,33,65,97,44,59,49,86,50,67,90,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU254+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n015.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 18 13:37:38 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.04 % [INFO] Parsing done (142ms).
% 1.24/1.04 % [INFO] Running in sequential loop mode.
% 1.75/1.25 % [INFO] eprover registered as external prover.
% 1.75/1.25 % [INFO] cvc4 registered as external prover.
% 1.75/1.25 % [INFO] Scanning for conjecture ...
% 1.85/1.31 % [INFO] Found a conjecture and 33 axioms. Running axiom selection ...
% 2.07/1.36 % [INFO] Axiom selection finished. Selected 26 axioms (removed 7 axioms).
% 2.19/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/1.39 % [INFO] Type checking passed.
% 2.19/1.39 % [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 ...
% 3.40/1.92 % External prover 'e' found a proof!
% 3.40/1.92 % [INFO] Killing All external provers ...
% 3.40/1.92 % Time passed: 1387ms (effective reasoning time: 877ms)
% 3.40/1.92 % 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)>
% 3.40/1.93 % Axioms used in derivation (26): fc1_zfmisc_1, t2_boole, rc3_funct_1, commutativity_k3_xboole_0, rc1_funct_1, t6_boole, rc2_funct_1, t106_zfmisc_1, t2_subset, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k3_xboole_0, l2_wellord1, fc1_xboole_0, d5_tarski, t1_subset, t7_boole, cc1_funct_1, cc2_funct_1, existence_m1_subset_1, commutativity_k2_tarski, dt_k2_wellord1, d6_wellord1, t16_wellord1, t8_boole, rc1_xboole_0
% 3.40/1.93 % No. of inferences in proof: 56
% 3.40/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1387 ms resp. 877 ms w/o parsing
% 3.84/1.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.84/1.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------