TSTP Solution File: SET011-1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET011-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 : Tue May 21 03:00:44 EDT 2024
% Result : Unsatisfiable 3.60s 2.14s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 48 ( 7 unt; 11 typ; 0 def)
% Number of atoms : 101 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 434 ( 48 ~; 64 |; 0 &; 322 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 98 ( 0 ^ 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_type,type,
intersection: $i > $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(aD_aDb_type,type,
aD_aDb: $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(member_of_1_not_of_2_type,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(difference_type,type,
difference: $i > $i > $i > $o ).
thf(k_type,type,
k: $i > $i > $i > $i ).
thf(aDb_type,type,
aDb: $i ).
thf(h_type,type,
h: $i > $i > $i > $i ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( difference @ B @ C @ D )
| ( member @ A @ D )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_difference_or_set2) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( difference @ B @ C @ D )
| ( member @ A @ D )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ B )
| ~ ( member @ D @ A )
| ( member @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ B )
| ~ ( member @ D @ A )
| ( member @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( h @ A @ B @ C ) @ C )
| ~ ( member @ ( h @ A @ B @ C ) @ B )
| ~ ( member @ ( h @ A @ B @ C ) @ A )
| ( intersection @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom3) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( h @ A @ B @ C ) @ C )
| ~ ( member @ ( h @ A @ B @ C ) @ B )
| ~ ( member @ ( h @ A @ B @ C ) @ A )
| ( intersection @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( k @ A @ B @ C ) @ C )
| ~ ( member @ ( k @ A @ B @ C ) @ A )
| ( member @ ( k @ A @ B @ C ) @ B )
| ( difference @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_axiom3) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( k @ A @ B @ C ) @ C )
| ~ ( member @ ( k @ A @ B @ C ) @ A )
| ( member @ ( k @ A @ B @ C ) @ B )
| ( difference @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
difference @ a @ aDb @ aD_aDb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_aDb) ).
thf(39,plain,
difference @ a @ aDb @ aD_aDb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( difference @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_difference) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( difference @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ ( h @ A @ B @ C ) @ C )
| ( intersection @ A @ B @ C )
| ( member @ ( h @ A @ B @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom2) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( h @ A @ B @ C ) @ C )
| ( intersection @ A @ B @ C )
| ( member @ ( h @ A @ B @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ ( h @ A @ B @ C ) @ C )
| ( intersection @ A @ B @ C )
| ( member @ ( h @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom1) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( h @ A @ B @ C ) @ C )
| ( intersection @ A @ B @ C )
| ( member @ ( h @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( k @ A @ B @ C ) @ B )
| ( member @ ( k @ A @ B @ C ) @ C )
| ( difference @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_axiom1) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( k @ A @ B @ C ) @ B )
| ( member @ ( k @ A @ B @ C ) @ C )
| ( difference @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ B @ C )
| ( member @ ( k @ A @ B @ C ) @ A )
| ( member @ ( k @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_axiom2) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ B @ C )
| ( member @ ( k @ A @ B @ C ) @ A )
| ( member @ ( k @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ~ ( difference @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_member_of_difference) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ~ ( difference @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
difference @ a @ b @ aDb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_b) ).
thf(40,plain,
difference @ a @ b @ aDb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
~ ( intersection @ a @ b @ aD_aDb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).
thf(19,plain,
~ ( intersection @ a @ b @ aD_aDb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,31,43,47,37,25,21,33,40,23,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SET011-1 : TPTP v8.2.0. Released v1.0.0.
% 0.04/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n006.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 11:33:54 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.90/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.08 % [INFO] Parsing done (167ms).
% 1.40/1.09 % [INFO] Running in sequential loop mode.
% 1.83/1.44 % [INFO] eprover registered as external prover.
% 1.83/1.44 % [INFO] cvc4 registered as external prover.
% 1.98/1.45 % [INFO] Scanning for conjecture ...
% 2.07/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 2.21/1.58 % [INFO] Axiom selection finished. Selected 17 axioms (removed 3 axioms).
% 2.21/1.61 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/1.61 % [INFO] Type checking passed.
% 2.21/1.62 % [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 ...
% 3.60/2.14 % External prover 'e' found a proof!
% 3.60/2.14 % [INFO] Killing All external provers ...
% 3.60/2.14 % Time passed: 1685ms (effective reasoning time: 1044ms)
% 3.60/2.14 % Axioms used in derivation (17): member_of_intersection_is_member_of_set2, a_minus_aDb, member_of_difference_or_set2, difference_axiom3, subsets_axiom2, member_of_both_is_member_of_intersection, difference_axiom2, a_minus_b, member_of_intersection_is_member_of_set1, difference_axiom1, intersection_axiom1, not_member_of_difference, member_of_difference, intersection_axiom3, intersection_axiom2, membership_in_subsets, subsets_axiom1
% 3.60/2.14 % No. of inferences in proof: 37
% 3.60/2.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1685 ms resp. 1044 ms w/o parsing
% 3.93/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.93/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------