TSTP Solution File: SET811+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 11:54:22 EDT 2023
% Result : Theorem 4.16s 2.16s
% Output : Refutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 41
% Syntax : Number of formulae : 63 ( 3 unt; 21 typ; 0 def)
% Number of atoms : 201 ( 12 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 634 ( 10 ~; 9 |; 65 &; 465 @)
% ( 17 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 4 con; 0-3 aty)
% Number of variables : 131 ( 0 ^; 122 !; 9 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(on_type,type,
on: $i ).
thf(equal_set_type,type,
equal_set: $i > $i > $o ).
thf(initial_segment_type,type,
initial_segment: $i > $i > $i > $i ).
thf(member_predicate_type,type,
member_predicate: $i ).
thf(least_type,type,
least: $i > $i > $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i > $o ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(set_type,type,
set: $i > $o ).
thf(strict_well_order_type,type,
strict_well_order: $i > $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(product_type,type,
product: $i > $i ).
thf(strict_order_type,type,
strict_order: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(suc_type,type,
suc: $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i ).
thf(12,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(142,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( union @ B @ C ) )
<=> ( ( member @ A @ B )
| ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(164,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( union @ B @ C ) )
=> ( ( member @ A @ B )
| ( member @ A @ C ) ) )
& ( ( ( member @ A @ B )
| ( member @ A @ C ) )
=> ( member @ A @ ( union @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ D @ ( initial_segment @ A @ B @ C ) )
<=> ( ( member @ D @ C )
& ( apply @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_segment) ).
thf(38,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ D @ ( initial_segment @ A @ B @ C ) )
=> ( ( member @ D @ C )
& ( apply @ B @ D @ A ) ) )
& ( ( ( member @ D @ C )
& ( apply @ B @ D @ A ) )
=> ( member @ D @ ( initial_segment @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( product @ B ) )
<=> ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( product @ B ) )
=> ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) ) )
& ( ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) )
=> ( member @ A @ ( product @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
<=> ( ( member @ A @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(156,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( intersection @ B @ C ) )
=> ( ( member @ A @ B )
& ( member @ A @ C ) ) )
& ( ( ( member @ A @ B )
& ( member @ A @ C ) )
=> ( member @ A @ ( intersection @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( apply @ member_predicate @ A @ B )
<=> ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_member) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( ( apply @ member_predicate @ A @ B )
=> ( member @ A @ B ) )
& ( ( member @ A @ B )
=> ( apply @ member_predicate @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( sum @ B ) )
<=> ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( sum @ B ) )
=> ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) ) )
& ( ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) )
=> ( member @ A @ ( sum @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( difference @ C @ B ) )
<=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
thf(150,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( difference @ C @ B ) )
=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) )
& ( ( ( member @ A @ C )
& ~ ( member @ A @ B ) )
=> ( member @ A @ ( difference @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( strict_well_order @ A @ B )
<=> ( ( strict_order @ A @ B )
& ! [C: $i] :
( ( ( subset @ C @ B )
& ? [D: $i] : ( member @ D @ C ) )
=> ? [D: $i] : ( least @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_well_order) ).
thf(72,plain,
! [A: $i,B: $i] :
( ( ( strict_well_order @ A @ B )
=> ( ( strict_order @ A @ B )
& ! [C: $i] :
( ( ( subset @ C @ B )
& ? [D: $i] : ( member @ D @ C ) )
=> ? [D: $i] : ( least @ D @ A @ C ) ) ) )
& ( ( ( strict_order @ A @ B )
& ! [C: $i] :
( ( ( subset @ C @ B )
& ? [D: $i] : ( member @ D @ C ) )
=> ? [D: $i] : ( least @ D @ A @ C ) ) )
=> ( strict_well_order @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: $i] :
( ( member @ A @ on )
=> ! [B: $i] :
( ( member @ B @ A )
=> ( equal_set @ B @ ( initial_segment @ B @ member_predicate @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV5) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( member @ A @ on )
=> ! [B: $i] :
( ( member @ B @ A )
=> ( equal_set @ B @ ( initial_segment @ B @ member_predicate @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ! [A: $i] :
( ( member @ A @ on )
=> ! [B: $i] :
( ( member @ B @ A )
=> ( equal_set @ B @ ( initial_segment @ B @ member_predicate @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_set @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( power_set @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( member @ A @ ( power_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i] :
( ( member @ A @ on )
<=> ( ( set @ A )
& ( strict_well_order @ member_predicate @ A )
& ! [B: $i] :
( ( member @ B @ A )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_number) ).
thf(49,plain,
! [A: $i] :
( ( ( member @ A @ on )
=> ( ( set @ A )
& ( strict_well_order @ member_predicate @ A )
& ! [B: $i] :
( ( member @ B @ A )
=> ( subset @ B @ A ) ) ) )
& ( ( ( set @ A )
& ( strict_well_order @ member_predicate @ A )
& ! [B: $i] :
( ( member @ B @ A )
=> ( subset @ B @ A ) ) )
=> ( member @ A @ on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( ( equal_set @ A @ B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( equal_set @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: $i] :
( ( set @ A )
=> ! [B: $i] :
( ( member @ B @ A )
=> ( set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_member) ).
thf(162,plain,
! [A: $i] :
( ( set @ A )
=> ! [B: $i] :
( ( member @ B @ A )
=> ( set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( member @ B @ ( suc @ A ) )
<=> ( member @ B @ ( union @ A @ ( singleton @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( ( member @ B @ ( suc @ A ) )
=> ( member @ B @ ( union @ A @ ( singleton @ A ) ) ) )
& ( ( member @ B @ ( union @ A @ ( singleton @ A ) ) )
=> ( member @ B @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( least @ C @ A @ B )
<=> ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( ( C = D )
| ( apply @ A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( ( least @ C @ A @ B )
=> ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( ( C = D )
| ( apply @ A @ C @ D ) ) ) ) )
& ( ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( ( C = D )
| ( apply @ A @ C @ D ) ) ) )
=> ( least @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
<=> ( ( A = B )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( unordered_pair @ B @ C ) )
=> ( ( A = B )
| ( A = C ) ) )
& ( ( ( A = B )
| ( A = C ) )
=> ( member @ A @ ( unordered_pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( singleton @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( singleton @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( member @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( strict_order @ A @ B )
<=> ( ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ~ ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_order) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( ( strict_order @ A @ B )
=> ( ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ~ ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) ) )
& ( ( ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ~ ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) )
=> ( strict_order @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(198,plain,
$false,
inference(cvc4,[status(thm)],[142,164,38,65,156,193,187,135,150,72,22,44,49,181,162,145,26,171,58,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n028.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 19:17:49 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.96/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.05 % [INFO] Parsing done (148ms).
% 1.29/1.06 % [INFO] Running in sequential loop mode.
% 1.71/1.28 % [INFO] eprover registered as external prover.
% 1.71/1.28 % [INFO] cvc4 registered as external prover.
% 1.71/1.29 % [INFO] Scanning for conjecture ...
% 1.90/1.35 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 2.06/1.39 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.06/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.06/1.44 % [INFO] Type checking passed.
% 2.06/1.45 % [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 ...
% 4.16/2.15 % External prover 'cvc4' found a proof!
% 4.16/2.15 % [INFO] Killing All external provers ...
% 4.16/2.16 % Time passed: 1628ms (effective reasoning time: 1089ms)
% 4.16/2.16 % 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)>
% 4.16/2.16 % Axioms used in derivation (19): power_set, unordered_pair, rel_member, union, strict_well_order, intersection, set_member, initial_segment, least, subset, equal_set, singleton, ordinal_number, difference, strict_order, sum, product, successor, empty_set
% 4.16/2.16 % No. of inferences in proof: 42
% 4.16/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1628 ms resp. 1089 ms w/o parsing
% 4.47/2.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.47/2.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------