TSTP Solution File: SET600+3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 03:03:05 EDT 2024
% Result : Theorem 3.72s 2.33s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 25 ( 7 unt; 5 typ; 0 def)
% Number of atoms : 65 ( 20 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 159 ( 7 ~; 3 |; 15 &; 107 @)
% ( 8 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 ^ 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_type,type,
union: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(9,axiom,
! [A: $i] :
( ( empty @ A )
<=> ! [B: $i] :
~ ( member @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
thf(56,plain,
! [A: $i] :
( ( ( empty @ A )
=> ! [B: $i] :
~ ( member @ B @ A ) )
& ( ! [B: $i] :
~ ( member @ B @ A )
=> ( empty @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,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)],[10]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(33,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)],[5]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(54,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( union @ A @ B )
= empty_set )
<=> ( ( A = empty_set )
& ( B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( union @ A @ B )
= empty_set )
<=> ( ( A = empty_set )
& ( B = empty_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i] :
( ( ( ( union @ A @ B )
= empty_set )
=> ( ( A = empty_set )
& ( B = empty_set ) ) )
& ( ( ( A = empty_set )
& ( B = empty_set ) )
=> ( ( union @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(23,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(30,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,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(47,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)],[7]) ).
thf(81,plain,
$false,
inference(e,[status(thm)],[56,61,33,44,54,11,23,30,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% 0.02/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n019.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 11:31:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.00/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.11 % [INFO] Parsing done (158ms).
% 1.26/1.12 % [INFO] Running in sequential loop mode.
% 1.83/1.48 % [INFO] eprover registered as external prover.
% 1.83/1.48 % [INFO] cvc4 registered as external prover.
% 1.91/1.49 % [INFO] Scanning for conjecture ...
% 2.02/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.02/1.61 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.17/1.64 % [INFO] Problem is first-order (TPTP FOF).
% 2.17/1.64 % [INFO] Type checking passed.
% 2.17/1.64 % [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 ...
% 3.72/2.32 % External prover 'e' found a proof!
% 3.72/2.32 % [INFO] Killing All external provers ...
% 3.72/2.32 % Time passed: 1843ms (effective reasoning time: 1192ms)
% 3.72/2.32 % 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)>
% 3.72/2.32 % Axioms used in derivation (8): reflexivity_of_subset, equal_member_defn, empty_set_defn, empty_defn, commutativity_of_union, equal_defn, union_defn, subset_defn
% 3.72/2.32 % No. of inferences in proof: 20
% 3.72/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1843 ms resp. 1192 ms w/o parsing
% 4.00/2.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.00/2.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------