TSTP Solution File: SET623+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET623+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 11:53:50 EDT 2023
% Result : Theorem 3.36s 1.92s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 21
% Syntax : Number of formulae : 38 ( 26 unt; 6 typ; 0 def)
% Number of atoms : 57 ( 29 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 257 ( 2 ~; 0 |; 8 &; 230 @)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 79 ( 0 ^; 79 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(symmetric_difference_type,type,
symmetric_difference: $i > $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(subset_type,type,
subset: $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(16,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(88,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( member @ C @ A )
<=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( difference @ ( union @ A @ B ) @ C )
= ( union @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( difference @ ( union @ A @ B ) @ C )
= ( union @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(81,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)],[15]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( difference @ ( difference @ A @ B ) @ C )
= ( difference @ A @ ( union @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).
thf(35,plain,
! [A: $i,B: $i,C: $i] :
( ( difference @ ( difference @ A @ B ) @ C )
= ( difference @ A @ ( union @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( difference @ B @ C ) )
= ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union1) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( difference @ B @ C ) )
= ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_union_intersection) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( symmetric_difference @ ( symmetric_difference @ A @ B ) @ C )
= ( symmetric_difference @ A @ ( symmetric_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th99) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( symmetric_difference @ ( symmetric_difference @ A @ B ) @ C )
= ( symmetric_difference @ A @ ( symmetric_difference @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( symmetric_difference @ ( symmetric_difference @ A @ B ) @ C )
= ( symmetric_difference @ A @ ( symmetric_difference @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( union @ ( union @ A @ B ) @ C )
= ( union @ A @ ( union @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).
thf(23,plain,
! [A: $i,B: $i,C: $i] :
( ( union @ ( union @ A @ B ) @ C )
= ( union @ A @ ( union @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(91,plain,
$false,
inference(cvc4,[status(thm)],[88,52,61,38,41,81,35,58,20,29,32,17,26,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET623+3 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.37 % Computer : n026.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu May 18 19:26:36 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.91/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (122ms).
% 1.21/0.99 % [INFO] Running in sequential loop mode.
% 1.61/1.21 % [INFO] eprover registered as external prover.
% 1.61/1.21 % [INFO] cvc4 registered as external prover.
% 1.61/1.22 % [INFO] Scanning for conjecture ...
% 1.76/1.28 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.76/1.30 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.91/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 1.91/1.33 % [INFO] Type checking passed.
% 1.91/1.33 % [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 ...
% 3.36/1.91 % External prover 'cvc4' found a proof!
% 3.36/1.91 % [INFO] Killing All external provers ...
% 3.36/1.92 % Time passed: 1385ms (effective reasoning time: 924ms)
% 3.36/1.92 % 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)>
% 3.36/1.92 % Axioms used in derivation (14): reflexivity_of_subset, difference_difference_union2, associativity_of_intersection, symmetric_difference_defn, equal_defn, difference_difference_union1, commutativity_of_symmetric_difference, subset_defn, associativity_of_union, difference_union_intersection, equal_member_defn, difference_distributes_over_union, commutativity_of_intersection, commutativity_of_union
% 3.36/1.92 % No. of inferences in proof: 32
% 3.36/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1385 ms resp. 924 ms w/o parsing
% 3.53/1.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.53/1.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------