TSTP Solution File: SET012+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:51:52 EDT 2023
% Result : Theorem 3.21s 1.75s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 24
% Syntax : Number of formulae : 38 ( 3 unt; 12 typ; 0 def)
% Number of atoms : 93 ( 9 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 288 ( 7 ~; 6 |; 22 &; 214 @)
% ( 10 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 0 ^; 62 !; 3 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(equal_set_type,type,
equal_set: $i > $i > $o ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i ).
thf(product_type,type,
product: $i > $i ).
thf(4,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(24,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)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( equal_set @ ( difference @ B @ ( difference @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI23) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( equal_set @ ( difference @ B @ ( difference @ B @ A ) ) @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( equal_set @ ( difference @ B @ ( difference @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( singleton @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(57,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)],[10]) ).
thf(12,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(74,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)],[12]) ).
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(41,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(8,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(48,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,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(64,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)],[11]) ).
thf(3,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(17,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)],[3]) ).
thf(13,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(80,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)],[13]) ).
thf(6,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(35,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)],[6]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_set @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(30,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(9,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(51,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)],[9]) ).
thf(90,plain,
$false,
inference(cvc4,[status(thm)],[24,14,57,74,41,48,64,17,80,35,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET012+4 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.14 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n009.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 18:45:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.94/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.95 % [INFO] Parsing done (109ms).
% 1.23/0.96 % [INFO] Running in sequential loop mode.
% 1.53/1.14 % [INFO] eprover registered as external prover.
% 1.53/1.14 % [INFO] cvc4 registered as external prover.
% 1.53/1.14 % [INFO] Scanning for conjecture ...
% 1.78/1.19 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.78/1.21 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.96/1.23 % [INFO] Problem is first-order (TPTP FOF).
% 1.96/1.24 % [INFO] Type checking passed.
% 1.96/1.24 % [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 ...
% 3.21/1.75 % External prover 'cvc4' found a proof!
% 3.21/1.75 % [INFO] Killing All external provers ...
% 3.21/1.75 % Time passed: 1231ms (effective reasoning time: 788ms)
% 3.21/1.75 % 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)>
% 3.21/1.75 % Axioms used in derivation (11): power_set, unordered_pair, union, intersection, empty_set, subset, equal_set, singleton, difference, sum, product
% 3.21/1.75 % No. of inferences in proof: 26
% 3.21/1.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1231 ms resp. 788 ms w/o parsing
% 3.51/1.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.51/1.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------