TSTP Solution File: SET776+4 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:54:17 EDT 2023
% Result : Theorem 4.73s 2.16s
% Output : Refutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 35
% Syntax : Number of formulae : 54 ( 3 unt; 18 typ; 0 def)
% Number of atoms : 249 ( 12 equ; 0 cnn)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 797 ( 10 ~; 6 |; 104 &; 574 @)
% ( 17 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 2 con; 0-3 aty)
% Number of variables : 161 ( 0 ^; 149 !; 12 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(pre_order_type,type,
pre_order: $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i > $o ).
thf(equal_set_type,type,
equal_set: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(product_type,type,
product: $i > $i ).
thf(partition_type,type,
partition: $i > $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(equivalence_type,type,
equivalence: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $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(equivalence_class_type,type,
equivalence_class: $i > $i > $i > $i ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( equivalence @ B @ A )
<=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( apply @ B @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ( apply @ B @ C @ D )
=> ( apply @ B @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( ( apply @ B @ C @ D )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
thf(142,plain,
! [A: $i,B: $i] :
( ( ( equivalence @ B @ A )
=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( apply @ B @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ( apply @ B @ C @ D )
=> ( apply @ B @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( ( apply @ B @ C @ D )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ C @ E ) ) ) ) )
& ( ( ! [C: $i] :
( ( member @ C @ A )
=> ( apply @ B @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ( apply @ B @ C @ D )
=> ( apply @ B @ D @ C ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( ( apply @ B @ C @ D )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ C @ E ) ) ) )
=> ( equivalence @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( sum @ B ) )
<=> ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(110,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)],[8]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
<=> ( ( A = B )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(216,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)],[17]) ).
thf(14,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(201,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( product @ B ) )
<=> ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(38,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)],[4]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( singleton @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(128,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)],[11]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( difference @ C @ B ) )
<=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(204,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)],[15]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( union @ B @ C ) )
<=> ( ( member @ A @ B )
| ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(103,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)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_set @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(123,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)],[10]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( pre_order @ B @ A )
& ! [D: $i,E: $i] :
( ( ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( apply @ C @ D @ E )
<=> ( ( apply @ B @ D @ E )
& ( apply @ B @ E @ D ) ) ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( member @ D @ A )
& ( member @ E @ A )
& ( member @ F @ A )
& ( member @ G @ A ) )
=> ( ( ( apply @ C @ D @ F )
& ( apply @ C @ E @ G )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII12) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( pre_order @ B @ A )
& ! [D: $i,E: $i] :
( ( ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( apply @ C @ D @ E )
<=> ( ( apply @ B @ D @ E )
& ( apply @ B @ E @ D ) ) ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( member @ D @ A )
& ( member @ E @ A )
& ( member @ F @ A )
& ( member @ G @ A ) )
=> ( ( ( apply @ C @ D @ F )
& ( apply @ C @ E @ G )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ F @ G ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( pre_order @ B @ A )
& ! [D: $i,E: $i] :
( ( ( member @ D @ A )
& ( member @ E @ A ) )
=> ( ( ( apply @ C @ D @ E )
=> ( ( apply @ B @ D @ E )
& ( apply @ B @ E @ D ) ) )
& ( ( ( apply @ B @ D @ E )
& ( apply @ B @ E @ D ) )
=> ( apply @ C @ D @ E ) ) ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( member @ D @ A )
& ( member @ E @ A )
& ( member @ F @ A )
& ( member @ G @ A ) )
=> ( ( ( apply @ C @ D @ F )
& ( apply @ C @ E @ G )
& ( apply @ B @ D @ E ) )
=> ( apply @ B @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
<=> ( ( member @ A @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(210,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)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ~ ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( pre_order @ A @ B )
<=> ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ 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/sandbox2/benchmark/theBenchmark.p',pre_order) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( ( pre_order @ A @ B )
=> ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ 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] :
( ( member @ C @ B )
=> ( apply @ A @ C @ 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 ) ) ) )
=> ( pre_order @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(32,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)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( partition @ A @ B )
<=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( subset @ C @ B ) )
& ! [C: $i] :
( ( member @ C @ B )
=> ? [D: $i] :
( ( member @ D @ A )
& ( member @ C @ D ) ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ? [E: $i] :
( ( member @ E @ C )
& ( member @ E @ D ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( ( partition @ A @ B )
=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( subset @ C @ B ) )
& ! [C: $i] :
( ( member @ C @ B )
=> ? [D: $i] :
( ( member @ D @ A )
& ( member @ C @ D ) ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ? [E: $i] :
( ( member @ E @ C )
& ( member @ E @ D ) )
=> ( C = D ) ) ) ) )
& ( ( ! [C: $i] :
( ( member @ C @ A )
=> ( subset @ C @ B ) )
& ! [C: $i] :
( ( member @ C @ B )
=> ? [D: $i] :
( ( member @ D @ A )
& ( member @ C @ D ) ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ A )
& ( member @ D @ A ) )
=> ( ? [E: $i] :
( ( member @ E @ C )
& ( member @ E @ D ) )
=> ( C = D ) ) ) )
=> ( partition @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/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)],[12]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ D @ ( equivalence_class @ C @ B @ A ) )
<=> ( ( member @ D @ B )
& ( apply @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
thf(226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ D @ ( equivalence_class @ C @ B @ A ) )
=> ( ( member @ D @ B )
& ( apply @ A @ C @ D ) ) )
& ( ( ( member @ D @ B )
& ( apply @ A @ C @ D ) )
=> ( member @ D @ ( equivalence_class @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(244,plain,
$false,
inference(cvc4,[status(thm)],[142,110,216,201,38,128,204,103,123,19,210,116,74,32,45,135,226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n031.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % 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 : Thu May 18 19:43:56 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.01 % [INFO] Parsing done (128ms).
% 1.38/1.02 % [INFO] Running in sequential loop mode.
% 1.85/1.24 % [INFO] eprover registered as external prover.
% 1.85/1.24 % [INFO] cvc4 registered as external prover.
% 1.85/1.24 % [INFO] Scanning for conjecture ...
% 1.85/1.31 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 2.16/1.36 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.16/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.45/1.40 % [INFO] Type checking passed.
% 2.45/1.40 % [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 ...
% 4.73/2.16 % External prover 'cvc4' found a proof!
% 4.73/2.16 % [INFO] Killing All external provers ...
% 4.73/2.16 % Time passed: 1623ms (effective reasoning time: 1132ms)
% 4.73/2.16 % 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)>
% 4.73/2.16 % Axioms used in derivation (16): power_set, unordered_pair, pre_order, intersection, empty_set, subset, equal_set, singleton, disjoint, difference, sum, product, equivalence, union, partition, equivalence_class
% 4.73/2.16 % No. of inferences in proof: 36
% 4.73/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1623 ms resp. 1132 ms w/o parsing
% 4.73/2.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.73/2.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------